String Theory Quotes

In life, people tend to wait for good things to come to them. And by waiting, they miss out. Usually, what you wish for doesn't fall in your lap; it falls somewhere nearby, and you have to recognize it, stand up, and put in the time and work it takes to get to it. This isn't because the universe is cruel. It's because the universe is smart. It has its own cat-string theory and knows we don't appreciate things that fall into our laps.

Some string theorists prefer to believe that string theory is too arcane to be understood by human beings, rather than consider the possibility that it might just be wrong.

There was quantum mechanics, string theory, and then there was the most mind-bending frontier of the natural world, women.

But my agent has a theory. She says every marriage is jerry-rigged. Even the ones that look reasonable from the outside are held together inside with chewing gum and wire and string.

I'm the Ted Bundy of string theory.

For string theory to make sense, the universe should have nine spacial dimensions and one time dimension, for a total of ten dimensions.

I've always had this theory that if I wanted something badly enough, the universe will make sure to keep it just out of my reach— either out of boredom or cruelty, like an invisible hand dangling stars on a string.

String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string.

Coincidence is merely the puppeteers’ curtain, hiding the hands that pull the world’s strings.

The most cherished goal in physics, as in bad romance novels, is unification.

There is much unexplained in the world. It behoves one to be wary at all times. Just when you think you've got the hang of it, along comes string theory, collateralised debt obligations or Björk's new album, and bam! You're as confused as you were when you first started.

... things are the way they are in our universe because if they Weren't, we would not be here to notice.

At this point I think we need to embrace the weird. High-five it. Give it our phone number.

But what is equally important, and sobering, is how often we fool ourselves. And we fool ourselves not only individually but en masse. The tendency of a group of human beings to quickly come to believe something that its individual members will later see as obviously false is truly amazing. Some of the worst tragedies of the last century happened because well-meaning people fell for easy solutions proposed by bad leaders.

String theory is rather like plumbing, in a way.

At that moment it would have been easier for me to spontaneously grasp quantum string theory

Lecter sits in his armchair with a big pad of butcher paper doing calculations. The pages are filled with the symbols both of astrophysics and particle physics. There are repeated efforts with the symbols of string theory. The few mathematicians who could follow him might say his equations begin brilliantly and then decline, doomed by wishful thinking. Dr. Lecter wants time to reverse — no longer should increasing entropy mark the direction of time. He wants increasing order to point the way”.

Perfection itself is a flaw, an odd knot in the cosmic fabric of evenly-braided imperfections.

When it comes to revolutionizing science, what matters is quality of thought, not quantity of true believers.

String theory makes sense to me because the universe is a symphony that creates harmony with the vibration of our strings.

Good ideas are not taken seriously enough when they come from people of low status in the academic world; conversely, the ideas of high-status people are often taken too seriously.

Dick Feynman was a genius of visualization (he was also no slouch with equations): he made a mental picture of anything he was working on. While others were writing blackboard-filling formulas to express the laws of elementary particles, he would just draw a picture and figure out the answer.

…The wonders of life and the universe are mere reflections of microscopic particles engaged in a pointless dance fully choreographed by the laws of physics.

There is about world-class athletes carving out exemptions from physical laws a transcendent beauty that makes manifest God in man.

Because of the speed of light. The known universe is about sixteen billion light-years across, and it’s still expanding. But the speed of light is only three hundred thousand kilometers per second, a snail’s pace. This means that light can never go from one end of the universe to the other. Since nothing can move faster than the speed of light, it follows that no information and motive force can go from one end of the universe to the other. If the universe were a person, his neural signals couldn’t cover his entire body; his brain would not know of the existence of his limbs, and his limbs would not know of the existence of the brain. Isn’t that paraplegia? The image in my mind is even worse: The universe is but a corpse puffing up.” “Interesting, Dr. Guan, very interesting!” “Other than the speed of light, three hundred thousand kilometers per second, there’s another three-based symptom.” “What do you mean?” “The three dimensions. In string theory, excepting time, the universe has ten dimensions. But only three are accessible at the macroscopic scale, and those three form our world. All the others are folded up in the quantum realm.

For three decades, Einstein sought a unified theory of physics, one that would interweave all of nature's forces and material constituents within a single theoretical tapestry. He failed. Now, at the dawn of the new millennium, proponents of string theory claim that the threads of this elusive unified tapestry finally have been revealed. String theory has the potential to show that all of the wondrous happenings in the universe—from the frantic dance of subatomic quarks to the stately waltz of orbiting binary stars, from the primordial fireball of the big bang to the majestic swirl of heavenly galaxies—are reflections of one grand physical principle, one master equation.

If patterns of ones and zeroes were "like" patterns of human lives and deaths, if everything about an individual could be represented in a computer record by a long strings of ones and zeroes, then what kind of creature could be represented by a long string of lives and deaths?

Bilderberg pulls the strings of every government and intelligence agency in the Western world.

All high mathematics serves to do is to beget higher mathematics.

On the way, I shared the backseat of Feyerabend's little sports car with the inflatable raft he kept there in case an 8-point earthquake came while he was on the Bay Bridge.

There is a husband who requires mileage receipts, another who wants sex at three a.m. One who forbids short haircuts, another who refuses to feed the pets. I would never put up with that, all the other wives think. Never. But my agent has a theory. She says every marriage is jerry-rigged. Even the ones that look reasonable from the outside are held together with chewing gum and wire and string.

The great tragedy of science—the slaying of a beautiful hypothesis by an ugly fact.” — THOMAS HENRY HUXLEY

We often say that the earth is a sphere, but to be precise, the term sphere refers only to the surface. The correct mathematical term for the solid earth is a ball.

In other words, the reason why the string theory cannot be solved is that twenty-first mathematics has not yet been discovered.

Kip Thorne says, “By 2020, physicists will understand the laws of quantum gravity, which will be found to be a variant of string theory.

in string theory, the dimensionality of space-time is fixed at ten dimensions.

(So string theory and M-theory are really the same theory, except that string theory is a reduction of eleven-dimensional M-theory to ten dimensions.)

By the time I began my study of physics in the early 1970s, the idea of unifying gravity with the other forces was as dead as the idea of continuous matter. It was a lesson in the foolishness of once great thinkers. Ernst Mach didn’t believe in atoms, James Clerk Maxwell believed in the aether, and Albert Einstein searched for a unified-field theory. Life is tough.

The dark-matter hypothesis is preferred mostly because the only other possibility—that we are wrong about Newton’s laws, and by extension general relativity—is too scary to contemplate.

The universe as a giant harpstring, oscillating in and out of existence! What note does it play, by the way? Passages from the Numerical Harmonies, I supposed?

It may well be that we spectators, who are not divinely giftes as athletes, are the only ones truly able to see, articulate and animate the experience of the gift we are denied.

So at 12:31pm, when he decided not to- when he came down, when the road opened- I did, too, my whole world, my whole mind went home with living proof of what I'd only before known in theory: that we are truly not alone in this, that our veins are absolutely strings tied to other people's kites, that our lives are connected. That my butterflies are never gone, they're just flying around in someone else's belly sometimes'.

Do you want a revolution in science? Do what businesspeople do when they want a technological revolution: Just change the rules a bit. Let in a few revolutionaries. Make the hierarchy a bit flatter, to give the young people more scope and freedom. Create some opportunities for high-risk/high-payoff people, so as to balance the huge investment you made in low-risk, incremental science. The technology companies and investment banks use this strategy. Why not try it in academia? The payoff could be discovering how the universe works.

We have one real candidate for changing the rules; this is string theory. In string theory the one-dimensional trajectory of a particle in spacetime is replaced by a two-dimensional orbit of a string. Such strings can be of any size, but under ordinary circumstances they are quite tiny, ... a value determined by comparing the predictions of the theory for Newton's constant and the fine structure constant to experimental values.

For the ten-dimensional universe, however, there are apparemtly millions of ways in which to curl up. To calculate which state the ten-dimensional universe prefers, we need to solve the field theory of strings using the theory of phase transitions, the most difficult problem in quantum theory.

We can measure the fine structure constant with very great precision, but so far none of our theories has provided an explanation of its measured value. One of the aims of superstring theory is to predict this quantity precisely. Any theory that could do that would be taken very seriously indeed as a potential 'Theory of Everything'.

There was a sense that the one true theory had been discovered. Nothing else was important or worth thinking about. Seminars devoted to string theory sprang up at many of the major universities and research institutes. At Harvard, the string theory seminar was called the Postmodern Physics seminar. This appellation was not meant ironically.

When someone answers a question about the foundations of a subject, it can change everything we know.

I do not consider myself a religious person, because I don't adhere to a particular religion or faith or prescribed beliefs, as did my father, who was a Baptist minister. And I am not an atheist, one who thinks that belief in anything beyond the here and now and the rational is delusion. I love science, but I allow for mystery, things that can never be proven by a rational mind. I am a person who thinks about the nature of the spirit when I write. I think about what can't be known and only imagined. I often sense a spirit or force or meaning beyond myself. I leave it open as to what the spirit is, but I continue to make guesses -- that it could be the universal binding of the emotion of love, or a joyful quality of humanity, or a collective unconscious that turns out to be a unified conscience. The spirit could be all those worshiped by all the religions, even those that deny the validity of others. It could be that we all exist in all ten dimensions of a string-theory universe and are seeding memories in all of them and occupy them simultaneously as memory. Or we exist only as thought and out perception that it is a physical world is a delusion. The nature of spirit could also be my mother and my grandmother and that they really do serve as my muses as I fondly imagine them doing at times. Or maybe the nature of the spirit is a freer imagination. I've often thought that imagination was the conduit to compassion, and compassion is a true spiritual nature. Whatever the spirit might be, I am not basing what I do in this life on any expected reward or punishment in the hereafter or thereafter. It is enough that I feel blessed -- and by whom or what I don't know -- but I receive it with gratitude that I am a writer and my work is to imagine all the possibilities.

These two discoveries, of relativity and of the quantum, each required us to break definitively with Newtonian physics. However, in spite of great progress over the century, they remain incomplete. Each has defects that point to a deeper theory. But the main reason each is incomplete is the existence of the other.

According to string theory, if we could examine these particles with even greater precision—a precision many orders of magnitude beyond our present technological capacity—we would find that each is not pointlike, but instead consists of a tiny one-dimensional loop. Like an infinitely thin rubber band, each particle contains a vibrating, oscillating, dancing filament that physicists, lacking Gell-Mann's literary flair, have named a string.

Quantum theory can be described as a new kind of language to be used in a dialogue between us and the systems we study with our instruments. This quantum language contains verbs that refer to our preparations and measurements and nouns that refer to what is then seen. It tells us nothing about what the world would be like in our absence.

One consequence of this formulation is that a physical principle that unites many smaller physical theories must autoomatically unite many seemingly unrelated branches of mathematics. This is precisely what string theory accomplishes. In fact, of all physical theories, string theory unites by far the largest number of branches of mathematics into a single coherent picture. Perhaps one of the by-products of the physicists' quest for unification will be the unification of mathematics as well.

(The string is extremely tiny, at the Planck length of 10 ^-33 cm, a billion billion times smaller than a proton, so all subatomic particles appear pointlike.) If we were to pluck this string, the vibration would change; the electron might turn into a neutrino. Pluck it again and it might turn into a quark. In fact, if you plucked it hard enough, it could turn into any of the known subatomic particles. Strings can interact by splitting and rejoining, thus creating the interactions we see among electrons and protons in atoms. In this way, through string theory, we can reproduce all the laws of atomic and nuclear physics. The "melodies" that can be written on strings correspond to the laws of chemistry. The universe can now be viewed as a vast symphony of strings.

String theory, therefore, is rich enough to explain all the fundamental laws of nature. Starting from a simple theory of a vibrating string, one can extract the theory of Einstein, Kaluza-Klein theory, supergravity, the Standard Model, and even GUT theory. It seems nothing less than a miracle that, starting from some purely geometric arguments from a string, one is able to rederive the entire progress of physics for the past 2 milleninia. All the theories so far discussed in this book are automatically included in string theory.

At the root of all physical reality is not “primary matter” or little atoms of “stuff.” Relativity theory in cosmology and the complementarity thesis in quantum physics suggest that the basic reality is some sort of hybrid “matter–energy.” Quantum field theory and string theory (if it survives as a physical theory, which now seems unlikely) suggest the even more radical idea that this reality is more energy-like than matter-like. Either result is sufficient to falsify materialism in anything like the form that dominated the first 300 years of modern science.

Over the last three decades, theorists have proposed at least a dozen new approaches. Each approach is motivated by a compelling hypothesis, but none has so far succeeded. In the realm of particle physics, these include Technicolor, preon models, and supersymmetry. In the realm of spacetime, they include twistor theory, causal sets, supergravity, dynamical triangulations, and loop quantum gravity. Some of these ideas are as exotic as they sound.

Almost anyone who loves tennis and follows the men’s tour on television has, over the last few years, had what might be termed Federer Moments. These are times, watching the young Swiss at play, when the jaw drops and eyes protrude and sounds are made that bring spouses in from other rooms to see if you’re OK.

Of course, the set of logically consistent mathematical structures is many times larger than the set of physical principles. Therefore, some mathematical structures, such as number theory (which some mathematicians claim to be the purest branch of mathematics), have never been incorporated into any physical theory. Some argue that this situation may always exist: Perhaps the human mind will always be able to conceive of logically consistent structures that cannot be expressed through any physical principle. However, there are indications that string theory may soon incorporate number theory into its structure as well.

Consider yourself and the cello. As you play the music moves out to the listener, and also enters the core of your own being, for somehow you are tuned to the cello. Well, I am persuaded that this is because you are a chord. I am a chord. Our DNA dictates our physicality-made up of billions of little notes-on a basic level. Add to that our geography, background et cetera, and you have your original score. Life is the layering of chords, but the underlying one that we are will never change. This brings us to string theory and love. Our personal chord resonates with the personal ones of others, and sometimes we encounter another person who is completely harmonious with us. It is a dominant, overwhelming attraction on the DNA level. However, such a person can appear to be our opposite-and that's where this 'opposites attract' notion comes from-because they have tuned their chord in a different way. In reality, we are attracted to the person we have chosen not to become, an alternative adjustment to a chord that is nearly the same as our own. The clashing portions of the chords sounding together advance the richness of it. So when you make love you aren't expressing emotions or showing affection, you are merging melodies. You are players in the same symphony.

According to string theory, if we could somehow magnify a point particle, we would actually see a small vibrating string. In fact, according to this theory, matter is nothing but the harmonies created by this vibrating string. Since there are an infinite number of harmonies that can be composed for the violin, there are an infinite number of forms of matter that can be constructed out of vibrating strings. This explains the richness of the particles in nature. Likewise, the laws of physics can be compared to the laws of harmony allowed on the string. The universe itself, composed of countless vibrating strings, would then be comparable to a symphony.

Let us return for a moment to Lady Lovelace’s objection, which stated that the machine can only do what we tell it to do. One could say that a man can "inject" an idea into the machine, and that it will respond to a certain extent and then drop into quiescence, like a piano string struck by a hammer. Another simile would be an atomic pile of less than critical size: an injected idea is to correspond to a neutron entering the pile from without. Each such neutron will cause a certain disturbance which eventually dies away. If, however, the size of the pile is sufficiently increased, the disturbance caused by such an incoming neutron will very likely go on and on increasing until the whole pile is destroyed. Is there a corresponding phenomenon for minds, and is there one for machines? There does seem to be one for the human mind. The majority of them seem to be "sub critical," i.e. to correspond in this analogy to piles of sub-critical size. An idea presented to such a mind will on average give rise to less than one idea in reply. A smallish proportion are supercritical. An idea presented to such a mind may give rise to a whole "theory" consisting of secondary, tertiary and more remote ideas. Animals’ minds seem to be very definitely sub-critical. Adhering to this analogy we ask, "Can a machine be made to be super-critical?

Some strings of marks or noises are meaningful sentences. It is an amazing fact that any normal person can instantly grasp the meaning of even a very long and novel sentence. Each meaningful sentence has parts that are themselves meaningful. Though initially attractive, the Referential Theory of Meaning faces several compelling objections.

Today the leading (and only) candidate for a theory of everything is string theory. But, again, a backlash has arisen. Opponents claim that to get a tenured position at a top university you have to work on string theory. If you don’t you will be unemployed. It’s the fad of the moment, and it’s not good for physics. I smile when I hear this criticism, because physics, like all human endeavors, is subject to fads and fashions. The fortunes of great theories, especially on the cutting edge of human knowledge, can rise and fall like hemlines. In fact, years ago the tables were turned; string theory was historically an outcast, a renegade theory, the victim of the bandwagon effect.

You don’t need a plan. Life will unfold in front of us, depending on which corner we turn down. I’m always discovering new places this way.” “So, no plan.” I prefer plans. No, I require them. I need to know how long something will take. When can I expect to be back at my hotel? Is where we’ll be walking safe? There are too many unknowns without a plan.

One night I begged Robin, a scientist by training, to watch Arthur Miller's 'Death of a Salesman' with me on PBS. He lasted about one act, then turned to me in horror: 'This is how you spend your days? Thinking about things like this?' I was ashamed. I could have been learning about string theory or how flowers pollinate themselves. I think his remark was the beginning of my crisis of faith. Like so many of my generation in graduate school, I had turned to literature as a kind of substitute for formal religion, which no longer fed my soul, or for therapy, which I could not afford.... I became interested in exploring the theory of nonfiction and in writing memoir, a genre that gives us access to that lost Middlemarch of reflection and social commentary.

The leading (and to my mind, only) candidate is called string theory, which posits the universe was not made of point particles but of tiny vibrating strings, with each note corresponding to a subatomic particle. If we had a microscope powerful enough, we could see that electrons, quarks, neutrinos, etc. are nothing but vibrations on minuscule loops resembling rubber bands. If we pluck the rubber band enough times and in different ways, we eventually create all the known subatomic particles in the universe. This means that all the laws of physics can be reduced to the harmonies of these strings. Chemistry is the melodies one can play on them. The universe is a symphony. And the mind of God, which Einstein eloquently wrote about, is cosmic music resonating throughout space-time.

For many years I have been saying that I would like to write a book (or series of books) called Physics for Mathematicians. Whenever I would tell people that, they would say, “Oh good, you're going to explain quantum mechanics, or string theory, or something like that”. And I would say, “Well that would be nice, but I can't begin to do that now; first I have to learn elementary physics, so the first thing I will be writing will be Mechanics for Mathematicians”. So then people would say, “Ah, so you're going to be writing about symplectic structures”, or something of that sort. And I would have to say, “No, I'm not trying to write a book about mathematics for mathematicians, I'm trying to write a book about physics for mathematicians”; …… it's elementary mechanics that I don't understand. … I mean, for example, that I don't understand this – lever. ... Most of us know the law of the lever, but this law is simply a quantitative statement of exactly how amazing the lever is, and doesn't give us a clue as to why it is true, how such a small force at one end can exert such a great force at the other. Now physicists all agree that Newton's Three Laws are the basis from which all of mechanics follows, but if you ask for an explanation of the lever in terms of these three laws, you will almost certainly not get a satisfactory answer.

Recent measurements reveal a universe consisting mostly of the unknown. Fully 70 percent of the matter density appears to be in the form of dark energy. Twenty-six percent is dark matter. Only 4 percent is ordinary matter. So less than 1 part in 20 is made out of matter we have observed experimentally or described in the standard model of particle physics. Of the other 96 percent, apart from the properties just mentioned, we know absolutely nothing.

In other words, if an observer looks at another frame of reference (like a moving train), he or she will still see that the speed of light is the same even though that frame of reference is moving relative to it. It is because of this symmetry that our standard theory of light, or electromagnetism, cannot accommodate a varying speed of light in empty space. But when a wave of light moves in a different medium, such as glass, Lorentz symmetry is no longer preserved, and light can change speed relative to empty space. This was the essence of Joao's contention. It could be that there is a quantum effect on space-time that fundamentally violates Einstein's cherished Lorentz symmetry, resulting in a variation of the speed of light in the early universe. As it turns out, the shape of extra dimensions in string theory can indeed cause certain constants, including the speed of light, to vary throughout the space-time fabric.

In the work of Ramanujan, the number 24 appears repeatedly. This is an example of what mathematicians call magic numbers, which continually appear, where we least expect them, for reasons that no one understands. Miraculously, Ramanujan's function also appears in string theory. The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory. In string theory, each of the 24 modes in the Ramanujan function corresponds to a physical vibration of the string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. (Since physicists add two more dimensions when they count the total number of vibrations appearing in a relativistic theory, this means that space-time must have 24 + 2 = 26 space-time dimensions.)

Love, that most banal of things, that most clichéd of religious motivations, had more power—Sol now knew—than did strong nuclear force or weak nuclear force or electromagnetism or gravity. Love was these other forces, Sol realized. The Void Which Binds, the subquantum impossibility that carried information from photon to photon, was nothing more or less than love. But could love—simple, banal love—explain the so-called anthropic principle which scientists had shaken their collective heads over for seven centuries and more—that almost infinite string of coincidences which had led to a universe that had just the proper number of dimensions, just the correct values on electron, just the precise rules for gravity, just the proper age to stars, just the right prebiologies to create just the perfect viruses to become just the proper DNAs—in short, a series of coincidences so absurd in their precision and correctness that they defied logic, defied understanding, and even defied religious interpretation. Love? For seven centuries the existence of Grand Unification Theories and hyperstring post-quantum physics and Core-given understanding of the universe as self-contained and boundless, without Big Bang singularities or corresponding endpoints, had pretty much eliminated any role of God—primitively anthropomorphic or sophisticatedly post-Einsteinian—even as a caretaker or pre-Creation former of rules. The modern universe, as machine and man had come to understand it, needed no Creator; in fact, allowed no Creator. Its rules allowed very little tinkering and no major revisions. It had not begun and would not end, beyond cycles of expansion and contraction as regular and self-regulated as the seasons on Old Earth. No room for love there.

The story I will tell could be read by some as a tragedy. To put it bluntly—and to give away the punch line—we have failed. We inherited a science, physics, that had been progressing so fast for so long that it was often taken as the model for how other kinds of science should be done. For more than two centuries, until the present period, our understanding of the laws of nature expanded rapidly. But today, despite our best efforts, what we know for certain about these laws is no more than what we knew back in the 1970s. How unusual is it for three decades to pass without major progress in fundamental physics? Even if we look back more than two hundred years, to a time when science was the concern mostly of wealthy amateurs, it is unprecedented.

The laws of physics can be reduced to the harmonies of these strings. Chemistry is the melodies one can play on them. The universe is a symphony. And the mind of God, which Einstein eloquently wrote about, is cosmic music resonating throughout space-time.

For me, the most beautiful aspects of physics are not the complicated math equations or even the ability of predicting how things will happen. What attracts me to physics is what it teaches us about the bigger picture. The general philosophical lessons that are embedded in physical laws are what excite me. For example, the fact that all particles and forces get unified within string theory teaches us about the unity underlying our universe. The amazingly vast collection of solutions to equations of string theory suggests that there may be many universes besides ours. What happened before the big bang, or was there a time before big bang? The “duality symmetry” in string theory, which exchanges small spaces with large spaces, suggests that perhaps as we go back in time the universe was effectively getting bigger instead of smaller. This suggests we came from other universes. Physics teaches us deep facts about our universe and our place in it. I hope I can add a little to this beautiful story. That is my goal.

The current crisis in particle physics springs from the fact that the theories have gone beyond the standard model in the last thirty years fall into two categories. Some were falsifiable, and they were falsified. The rest are untested-either because they make no clean predictions or because the predictions they do make are not testable with current technology. Over the last three decades, theorists have proposed at least a dozen new approaches. Each approach is motivated by a compelling hypothesis, but none has so far succeeded. In the realm of particle physics, these include Technicolor, preon models, and supersymmetry. In the realm of spacetime, they include twistor theory, causal sets, supergravity, dynamical triangulations, and loop quantum gravity. Some of these ideas are as exotic as they sound

If we had a microscope powerful enough, we could see that electrons, quarks, neutrinos, etc. are nothing but vibrations on minuscule loops resembling rubber bands. If we pluck the rubber band enough times and in different ways, we eventually create all the known subatomic particles in the universe. This means that all the laws of physics can be reduced to the harmonies of these strings. Chemistry is the melodies one can play on them. The universe is a symphony. And the mind of God, which Einstein eloquently wrote about, is cosmic music resonating throughout space-time.

Every culture has its own creation myth, its own cosmology. And in some respects every cosmology is true, even if I might flatter myself in assuming mine is somehow truer because it is scientific. But it seems to me that no culture, including scientific culture, has cornered the market on definitive answers when it comes to the ultimate questions. Science may couch its models in the language of mathematics and observational astronomy, while other cultures use poetry and sacrificial propitiations to defend theirs. But in the end, no one knows, at least not yet. The current flux in the state of scientific cosmology attests to this, as we watch physicists and astronomers argue over string theory and multiverses and the cosmic inflation hypothesis. Many of the postulates of modern cosmology lie beyond, or at least at the outer fringes, of what can be verified through observation. As a result, aesthetics—as reflected by the “elegance” of the mathematical models—has become as important as observation in assessing the validity of a cosmological theory. There is the assumption, sometimes explicit and sometimes not, that the universe is rationally constructed, that it has an inherent quality of beauty, and that any mathematical model that does not exemplify an underlying, unifying simplicity is to be considered dubious if not invalid on such criteria alone. This is really nothing more than an article of faith; and it is one of the few instances where science is faith-based, at least in its insistence that the universe can be understood, that it “makes sense.” It is not entirely a faith-based position, in that we can invoke the history of science to support the proposition that, so far, science has been able to make sense, in a limited way, of much of what it has scrutinized. (The psychedelic experience may prove to be an exception.)

Unfortunately, no one has ever successfully postulated a super-symmetry holding between two known particles. Instead, in all the supersymmetric theories the numbers of particles are at least doubled. A new superpartner is simply postulated to go along with each known particle. Not only are there squarks and sleptons and photinos, there are also sneutrinos to partner the neutrinos, Higgsinos with the Higgs, and gravitinos to go with the gravitons. Two by two, a regular Noah's ark of particles. Sooner or later, tangled in the web of new snames and naminos, you begin to feel like Sbozo the clown. Or Bozo the clownino. Or swhatever.

Let us return for a moment to Lady Lovelace’s objection, which stated that the machine can only do what we tell it to do. One could say that a man can “inject” an idea into the machine, and that it will respond to a certain extent and then drop into quiescence, like a piano string struck by a hammer. Another simile would be an atomic pile of less than critical size: an injected idea is to correspond to a neutron entering the pile from without. Each such neutron will cause a certain disturbance which eventually dies away. If, however, the size of the pile is sufficiently increased, the disturbance caused by such an incoming neutron will very likely go on and on increasing until the whole pile is destroyed. Is there a corresponding phenomenon for minds, and is there one for machines? There does seem to be one for the human mind. The majority of them seem to be “sub-critical,” i.e. to correspond in this analogy to piles of sub-critical size. An idea presented to such a mind will on average give rise to less than one idea in reply. A smallish proportion are supercritical. An idea presented to such a mind may give rise to a whole “theory” consisting of secondary, tertiary and more remote ideas. Animals’ minds seem to be very definitely sub-critical. Adhering to this analogy we ask, “Can a machine be made to be super-critical?

In 1994 another bombshell was dropped. Edward Witten of Princeton's Institute for Advanced Study and Paul Townsend of Cambridge University speculated that all five string theories were in fact the same theory-but only if we add an eleventh dimension. From the vantage point of the eleventh dimension, all five different theories collapsed into one! The theory was unique after all, but only if we ascended to the mountaintop of the eleventh dimension. In the eleventh dimension a new mathematical object can exist, called the membrane (e.g., like the surface of a sphere). Here was the amazing observation: if one dropped from eleven dimensions down to ten dimensions, all five string theories would emerge, starting from a single membrane. Hence all five string theories were just different ways of moving a membrane down from eleven to ten dimensions. (To visualize this, imagine a beach ball with a rubber band stretched around the equator. Imagine taking a pair of scissors and cutting the beach ball twice, once above and once below the rubber band, thereby lopping off the top and bottom of the beach ball. All that is left is the rubber band, a string. In the same way, if we curl up the eleventh dimension, all that is left of a membrane is its equator, which is the string. In fact, mathematically there are five ways in which this slicing can occur, leaving us with five different string theories in ten dimensions.)

The use of spontaneous symmetry breaking in a fundamental theory was to have profound consequences, not just for the laws of nature but for the larger question of what a law of nature is. Before this, it was thought that the properties of the elementary particles are determined directly by eternally given laws of nature. But in a theory with spontaneous symmetry breaking, a new element enters, which is that the properties of the elementary particles depend in part on history and environment. The symmetry may break in different ways, depending on conditions like density and temperature. More generally, the properties of the elementary particles depend not just on the equations of the theory but on which solution to those equations applies to our universe.

I received comments on how extraordinary it was that I could keep up speaking for exactly 45 minutes. Indeed, in an age of soundbites lasting some seconds and of quick quotes in the news, all those minutes do seem like an eternity, easy to get lost in. Yet, wait a moment. Television is not the only place where speeches are given. Some hundred thousand teachers teach every day. They all speak 45 minutes, more times a day. They have been doing this for years. Every teacher knows exactly when the time will be over and that by then his speech will need to come to a natural end. It is this tension that determines the success of a lesson. It is a sign of the times that we forget these daily achievements in education. A million students daily attend several ‘live’ lectures and this in secondary education alone. These are high ratings!

It is the best of times in physics. Physicists are on the verge of obtaining the long-sought theory of everything. In a few elegant equations, perhaps concise enough to be emblazoned on a T-shirt, this theory will reveal how the universe began and how it will end. The key insight is that the smallest constituents of the world are not particles, as had been supposed since ancient times, but “strings”—tiny strands of energy. By vibrating in different ways, these strings produce the essential phenomena of nature, the way violin strings produce musical notes. String theory isn’t just powerful; it’s also mathematically beautiful. All that remains to be done is to write down the actual equations. This is taking a little longer than expected. But, with almost the entire theoretical-physics community working on the problem—presided over by a sage in Princeton, New Jersey—the millennia-old dream of a final theory is sure to be realized before long. It is the worst of times in physics. For more than a generation, physicists have been chasing a will-o’-the-wisp called string theory. The beginning of this chase marked the end of what had been three-quarters of a century of progress. Dozens of string-theory conferences have been held, hundreds of new Ph.D.’s have been minted, and thousands of papers have been written. Yet, for all this activity, not a single new testable prediction has been made; not a single theoretical puzzle has been solved. In fact, there is no theory so far—just a set of hunches and calculations suggesting that a theory might exist. And, even if it does, this theory will come in such a bewildering number of versions that it will be of no practical use: a theory of nothing. Yet the physics establishment promotes string theory with irrational fervor, ruthlessly weeding dissenting physicists from the profession. Meanwhile, physics is stuck in a paradigm doomed to barrenness.

During a British conference on comparative religions, experts from around the world debated what, if any, belief was unique to the Christian faith. They began eliminating possibilities. Incarnation? Other religions had different versions of gods appearing in human form. Resurrection? Again, other religions had accounts of return from death. The debate went on for some time until C. S. Lewis wandered into the room. “What’s the rumpus about?” He asked, and heard in reply that his colleagues were discussing Christianity’s unique contribution among world religions. Lewis responded, “Oh, that’s easy. It’s grace.” After some discussion, the conferees had to agree. The notion of God’s love coming to us free of charge, no strings attached, seems to go against every instinct of humanity. The Buddhist eight-fold path, the Hindu doctrine of karma, the Jewish covenant, and Muslim code of law—each of these offers a way to earn approval. Only Christianity dares to make God’s love unconditional

Groupthink members see themselves as part of an in-group working against an outgroup opposed to their goals. You can tell if a group suffers from groupthink if it: overestimates its invulnerability or high moral stance, collectively rationalizes the decisions it makes, demonizes or stereotypes outgroups and their leaders, has a culture of uniformity where individuals censor themselves and others so that the facade of group unanimity is maintained, and contains members who take it upon themselves to protect the group leader by keeping information, theirs or other group members’, from the leader.

I want to quote that poem in something I'm writing," he explained, "and can you tell me the last line of it ? " Lou answered mechanically, as if he had pressed a button: "Death is not a way out of it!" "A very strange theory, that about death," he said. "I wonder if there's anything in it. It would really be too easy if we could get out of our troubles in so simple a fashion. It has always seemed to me that nothing can ever be destroyed. The problems of life are really put together ingeniously in order to baffle one, like a chess problem. We can't untie a real knot in a closed piece of string without the aid of the fourth dimension; but we can disentangle the complexities caused by dipping the string in water-and such things," he added, with an almost malicious gravity in his tone. I knew what he meant. " It might very well be," he continued, " that when we fail to solve the puzzles of life, they remain with us. We have to do them sooner or later ; and it seems reasonable to suppose that the problems of life ought to be solved during life, while we have to our hands the apparatus in which they arose. We might find that after death the problems were unaltered, but that we were impotent to deal with them. Did you ever meet any one that had been indiscreet about taking drugs ? Presumably not. Well, take my word for it, those people get into a state which is in many ways very like death. And the tragic thing about the situation is this ; that they started taking the drugs because life, in one way or another, was one too many for them. And what is the result ? The drugs have not in the least relieved the monotony of life or whatever their trouble was, and yet they have got into a state very like that of death, in which they are impotent to struggle. No, we must conquer life by living it to the full, and then we can go to meet death with a certain prestige. We can face that adventure as we've faced the others.

The third method of dealing with large-scale moral dilemmas is to weave conspiracy theories. How does the global economy function, and is it good or bad? That question is too complicated to grasp. It is far easier to imagine that twenty multibillionaires are pulling the strings behind the scenes, controlling the media and fomenting wars in order to enrich themselves. This is almost always a baseless fantasy. The contemporary world is too complicated, not only for our sense of justice but also for our managerial abilities. No one—including the multibillionaires, the CIA, the Freemasons, and the Elders of Zion—really understands what is going on in the world. So no one is capable of pulling the strings effectively.

Or think of the tale of the blind men who encounter an elephant for the first time. One wise man, touching the ear of the elephant, declares the elephant is flat and two-dimensional like a fan. Another wise man touches the tail and assumes the elephant is like rope or a one-dimensional string. Another, touching a leg, concludes the elephant is a three-dimensional drum or a cylinder. But actually, if we step back and rise into the third dimension, we can see the elephant as a three-dimensional animal. In the same way, the five different string theories are like the ear, tail, and leg, but we still have yet to reveal the full elephant, M-theory. Holographic Universe As we mentioned, with time new layers have been uncovered in string theory. Soon after M-theory was proposed in 1995, another astonishing discovery was made by Juan Maldacena in 1997. He jolted the entire physics community by showing something that was once considered impossible: that a supersymmetric Yang-Mills theory, which describes the behavior of subatomic particles in four dimensions, was dual, or mathematically equivalent, to a certain string theory in ten dimensions. This sent the physics world into a tizzy. By 2015, there were ten thousand papers that referred to this paper, making it by far the most influential paper in high-energy physics. (Symmetry and duality are related but different. Symmetry arises when we rearrange the components of a single equation and it remains the same. Duality arises when we show that two entirely different theories are actually mathematically equivalent. Remarkably, string theory has both of these highly nontrivial features.)

Music of the Grid: A Poem in Two Equations _________________________ The masses of particles sound the frequencies with which space vibrates, when played. This Music of the Grid betters the old mystic mainstay, "Music of the Spheres," both in fantasy and in realism. LET US COMBINE Einstein's second law m=E/C^2 (1) with another fundamental equation, the Planck-Einstein-Schrodinger formula E = hv The Planck-Einstein-Schrodinger formula relates the energy E of a quantum-mechanical state to the frequency v at which its wave function vibrates. Here h is Planck's constant. Planck introduced it in his revolutionary hypothesis (1899) that launched quantum theory: that atoms emit or absorb light of frequency v only in packets of energy E = hv. Einstein went a big step further with his photon hypothesis (1905): that light of frequency v is always organized into packets with energy E = hv. Finally Schrodinger made it the basis of his basic equation for wave functions-the Schrodinger equation (1926). This gave birth to the modern, universal interpretation: the wave function of any state with energy E vibrates at a frequency v given by v = E/h. By combining Einstein with Schrodinger we arrive at a marvelous bit of poetry: (*) v = mc^2/h (*) The ancients had a concept called "Music of the Spheres" that inspired many scientists (notably Johannes Kepler) and even more mystics. Because periodic motion (vibration) of musical instruments causes their sustained tones, the idea goes, the periodic motions of the planets, as they fulfill their orbits, must be accompanied by a sort of music. Though picturesque and soundscape-esque, this inspiring anticipation of multimedia never became a very precise or fruitful scientific idea. It was never more than a vague metaphor, so it remains shrouded in equation marks: "Music of the Spheres." Our equation (*) is a more fantastic yet more realistic embodiment of the same inspiration. Rather than plucking a string, blowing through a reed, banging on a drumhead, or clanging a gong, we play the instrument that is empty space by plunking down different combinations of quarks, gluons, electrons, photons,... (that is, the Bits that represent these Its) and let them settle until they reach equilibrium with the spontaneous activity of Grid. Neither planets nor any material constructions compromise the pure ideality of our instrument. It settles into one of its possible vibratory motions, with different frequencies v, depending on how we do the plunking, and with what. These vibrations represent particles of different mass m, according to (*). The masses of particles sound the Music of the Grid.

[...]a man and a boy, side by side on a yellow Swedish sofa from the 1950s that the man had bought because it somehow reminded him of a zoot suit, watching the A’s play Baltimore, Rich Harden on the mound working that devious ghost pitch, two pairs of stocking feet, size 11 and size 15, rising from the deck of the coffee table at either end like towers of the Bay Bridge, between the feet the remains in an open pizza box of a bad, cheap, and formerly enormous XL meat lover’s special, sausage, pepperoni, bacon, ground beef, and ham, all of it gone but crumbs and parentheses of crusts left by the boy, brackets for the blankness of his conversation and, for all the man knew, of his thoughts, Titus having said nothing to Archy since Gwen’s departure apart from monosyllables doled out in response to direct yes-or-nos, Do you like baseball? you like pizza? eat meat? pork?, the boy limiting himself whenever possible to a tight little nod, guarding himself at his end of the sofa as if riding on a crowded train with something breakable on his lap, nobody saying anything in the room, the city, or the world except Bill King and Ken Korach calling the plays, the game eventless and yet blessedly slow, player substitutions and deep pitch counts eating up swaths of time during which no one was required to say or to decide anything, to feel what might conceivably be felt, to dread what might be dreaded, the game standing tied at 1 and in theory capable of going on that way forever, or at least until there was not a live arm left in the bullpen, the third-string catcher sent in to pitch the thirty-second inning, batters catnapping slumped against one another on the bench, dead on their feet in the on-deck circle, the stands emptied and echoing, hot dog wrappers rolling like tumbleweeds past the diehards asleep in their seats, inning giving way to inning as the dawn sky glowed blue as the burner on a stove, and busloads of farmhands were brought in under emergency rules to fill out the weary roster, from Sacramento and Stockton and Norfolk, Virginia, entire villages in the Dominican ransacked for the flower of their youth who were loaded into the bellies of C-130s and flown to Oakland to feed the unassuageable appetite of this one game for batsmen and fielders and set-up men, threat after threat giving way to the third out, weak pop flies, called third strikes, inning after inning, week after week, beards growing long, Christmas coming, summer looping back around on itself, wars ending, babies graduating from college, and there’s ball four to load the bases for the 3,211th time, followed by a routine can of corn to left, the commissioner calling in varsity teams and the stars of girls’ softball squads and Little Leaguers, Archy and Titus sustained all that time in their equally infinite silence, nothing between them at all but three feet of sofa;

Out of the hundreds of examples that one might choose, take this question: Which of the three great allies, the U.S.S.R., Britain and the USA, has contributed most to the defeat of Germany? In theory, it should be possible to give a reasoned and perhaps even a conclusive answer to this question. In practice, however, the necessary calculations cannot be made, because anyone likely to bother his head about such a question would inevitably see it in terms of competitive prestige. He would therefore start by deciding in favour of Russia, Britain or America as the case might be, and only after this would begin searching for arguments that seemed to support his case. And there are whole strings of kindred questions to which you can only get an honest answer from someone who is indifferent to the whole subject involved, and whose opinion on it is probably worthless in any case. Hence, partly, the remarkable failure in our time of political and military prediction.

Two Types of Subatomic Particles Fermions (matter) Bosons (forces) electron, quark, photon, graviton, neutrino, proton Yang-Mills Bunji Sakita and Jean-Loup Gervais then demonstrated that string theory had a new type of symmetry, called supersymmetry. Since then, supersymmetry has been expanded so that it is now the largest symmetry ever found in physics. As we have emphasized, beauty to a physicist is symmetry, which allows us to find the link between different particles. All the particles of the universe could then be unified by supersymmetry. As we have emphasized, a symmetry rearranges the components of an object, leaving the original object the same. Here, one is rearranging the particles in our equations so that fermions are interchanged with bosons and vice versa. This becomes the central feature of string theory, so that the particles of the entire universe can be rearranged into one another. This means that each particle has a super partner, called a sparticle, or super particle. For example, the super partner of the electron is called the selectron. The super partner of the quark is called the squark. The superpartner of the lepton (like the electron or neutrino) is called the slepton. But in string theory, something remarkable happens. When calculating quantum corrections to string theory, you have two separate contributions. You have quantum corrections coming from fermions and also bosons. Miraculously, they are equal in size, but occur with the opposite sign. One term might have a positive sign, but there is another term that is negative. In fact, when they are added together, these terms cancel against each other, leaving a finite result. The marriage between relativity and the quantum theory has dogged physicists for almost a century, but the symmetry between fermions and bosons, called supersymmetry, allows us to cancel many of these infinities against each other. Soon, physicists discovered other means of eliminating these infinities, leaving a finite result. So this is the origin of all the excitement surrounding string theory: it can unify gravity with the quantum theory. No other theory can make this claim. This may satisfy Dirac’s original objection. He hated renormalization theory because, in spite of its fantastic and undeniable successes, it involved adding and subtracting quantities that were infinite in size. Here, we see that string theory is finite all by itself, without renormalization

As physicist Edward Witten once said, “String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it’s obligatory in string theory.” Ten Dimensions But as the theory began to evolve, more and more fantastic, totally unexpected features began to be revealed. For example, it was found that the theory can only exist in ten dimensions! This shocked physicists, because no one had ever seen anything like it. Usually, any theory can be expressed in any dimension you like. We simply discard these other theories because we obviously live in a three-dimensional world. (We can only move forward, sideways, and up and down. If we add time, then it takes four dimensions to locate any event in the universe. If we want to meet someone in Manhattan, for example, we might say, Let’s meet at the corner of 5th Avenue and 42nd Street, on the tenth floor, at noon. However, moving in dimensions beyond four is impossible for us, no matter how we try. In fact, our brains cannot even visualize how to move in higher dimensions. Therefore all the research done in higher-dimensional string theory is done using pure mathematics.) But in string theory, the dimensionality of space-time is fixed at ten dimensions. The theory breaks down mathematically in other dimensions. I still remember the shock that physicists felt when string theory posited that we live in a universe of ten dimensions. Most physicists saw this as proof that the theory was wrong. When John Schwarz, one of the leading architects of string theory, was in the elevator at Caltech, Richard Feynman would prod him, asking, “Well, John, and how many dimensions are you in today?” Yet over the years, physicists gradually began to show that all rival theories suffered from fatal flaws. For example, many could be ruled out because their quantum corrections were infinite or anomalous (that is, mathematically inconsistent). So over time, physicists began to warm up to the idea that perhaps our universe might be ten-dimensional after all. Finally, in 1984, John Schwarz and Michael Green showed that string theory was free of all the problems that had doomed previous candidates for a unified field theory. If string theory is correct, then the universe might have originally been ten-dimensional. But the universe was unstable and six of these dimensions somehow curled up and became too small to be observed. Hence, our universe might actually be ten-dimensional, but our atoms are too big to enter these tiny higher dimensions.

But so far, we have only discussed applying quantum mechanics to the matter that moves within the gravity fields of Einstein’s theory. We have not discussed a much more difficult question: applying quantum mechanics to gravity itself in the form of gravitons. And this is where we encounter the biggest question of all: finding a quantum theory of gravity, which has frustrated the world’s great physicists for decades. So let us review what we have learned so far. We recall that when we apply the quantum theory to light, we introduce the photon, a particle of light. As this photon moves, it is surrounded by electric and magnetic fields that oscillate and permeate space and obey Maxwell’s equations. This is the reason why light has both particle-like and wavelike properties. The power of Maxwell’s equations lies in their symmetries—that is, the ability to turn electric and magnetic fields into each other. When the photon bumps into electrons, the equation that describes this interaction yields results that are infinite. However, using the bag of tricks devised by Feynman, Schwinger, Tomonaga, and many others, we are able to hide all the infinities. The resulting theory is called QED. Next, we applied this method to the nuclear force. We replaced the original Maxwell field with the Yang-Mills field, and replaced the electron with a series of quarks, neutrinos, etc. Then we introduced a new bag of tricks devised by ’t Hooft and his colleagues to eliminate all the infinities once again. So three of the four forces of the universe could now be unified into a single theory, the Standard Model. The resulting theory was not very pretty, since it was created by cobbling together the symmetries of the strong, weak, and electromagnetic forces, but it worked. But when we apply this tried-and-true method to gravity, we have problems. In theory, a particle of gravity should be called the graviton. Similar to the photon, it is a point particle, and as it moves at the speed of light, it is surrounded by waves of gravity that obey Einstein’s equations. So far, so good. The problem occurs when the graviton bumps into other gravitons and also atoms. The resulting collision creates infinite answers. When one tries to apply the bag of tricks painfully formulated over the last seventy years, we find that they all fail. The greatest minds of the century have tried to solve this problem, but no one has been successful. Clearly, an entirely new approach must be used, since all the easy ideas have been investigated and discarded. We need something truly fresh and original. And that leads us to perhaps the most controversial theory in physics, string theory, which might just be crazy enough to be the theory of everything.

A great deal of effort has been devoted to explaining Babel. Not the Babel event -- which most people consider to be a myth -- but the fact that languages tend to diverge. A number of linguistic theories have been developed in an effort to tie all languages together." "Theories Lagos tried to apply to his virus hypothesis." "Yes. There are two schools: relativists and universalists. As George Steiner summarizes it, relativists tend to believe that language is not the vehicle of thought but its determining medium. It is the framework of cognition. Our perceptions of everything are organized by the flux of sensations passing over that framework. Hence, the study of the evolution of language is the study of the evolution of the human mind itself." "Okay, I can see the significance of that. What about the universalists?" "In contrast with the relativists, who believe that languages need not have anything in common with each other, the universalists believe that if you can analyze languages enough, you can find that all of them have certain traits in common. So they analyze languages, looking for such traits." "Have they found any?" "No. There seems to be an exception to every rule." "Which blows universalism out of the water." "Not necessarily. They explain this problem by saying that the shared traits are too deeply buried to be analyzable." "Which is a cop out." "Their point is that at some level, language has to happen inside the human brain. Since all human brains are more or less the same --" "The hardware's the same. Not the software." "You are using some kind of metaphor that I cannot understand." "Well, a French-speaker's brain starts out the same as an English-speaker's brain. As they grow up, they get programmed with different software -- they learn different languages." "Yes. Therefore, according to the universalists, French and English -- or any other languages -- must share certain traits that have their roots in the 'deep structures' of the human brain. According to Chomskyan theory, the deep structures are innate components of the brain that enable it to carry out certain formal kinds of operations on strings of symbols. Or, as Steiner paraphrases Emmon Bach: These deep structures eventually lead to the actual patterning of the cortex with its immensely ramified yet, at the same time, 'programmed' network of electrochemical and neurophysiological channels." "But these deep structures are so deep we can't even see them?" "The universalists place the active nodes of linguistic life -- the deep structures -- so deep as to defy observation and description. Or to use Steiner's analogy: Try to draw up the creature from the depths of the sea, and it will disintegrate or change form grotesquely.

Similarly, we look for echoes from the tenth and eleventh dimension. Perhaps evidence for string theory is hidden all around us, but we have to listen for its echoes, rather than try to observe it directly. For example, one possible signal from hyperspace is the existence of dark matter. Until recently, it was widely believed that the universe is mainly made of atoms. Astronomers have been shocked to find that only 4.9 percent of the universe is made of atoms like hydrogen and helium. Actually, most of the universe is hidden from us, in the form of dark matter and dark energy. (We recall that dark matter and dark energy are two distinct things. Twenty-six point eight percent of the universe is made of dark matter, which is invisible matter that surrounds the galaxies and keep them from flying apart. And 68.3 percent of the universe is made of dark energy, which is even more mysterious, the energy of empty space that is driving the galaxies apart.) Perhaps evidence for the theory of everything lies hidden in this invisible universe. Search for Dark Matter Dark matter is strange, it is invisible, yet it holds the Milky Way galaxy together. But since it has weight and no charge, if you tried to hold dark matter in your hand it would sift through your fingers as if they weren’t there. It would fall right through the floor, through the core of the Earth, and then to the other side of the Earth, where gravity would eventually cause it to reverse course and fall back to your location. It would then oscillate between you and the other side of the planet, as if the Earth weren’t there. As strange as dark matter is, we know it must exist. If we analyze the spin of the Milky Way galaxy and use Newton’s laws, we find that there is not enough mass to counteract the centrifugal force. Given the amount of mass we see, the galaxies in the universe should be unstable and they should fly apart, but they have been stable for billions of years. So we have two choices: either Newton’s equations are incorrect when applied to galaxies, or else there is an unseen object that is keeping the galaxies intact. (We recall that the planet Neptune was found in the same way, by postulating a new planet that explained Uranus’s deviations from a perfect ellipse.) At present, one leading candidate for dark matter is called the weakly interacting massive particles (WIMPs). Among them, one likely possibility is the photino, the supersymmetric partner of the photon. The photino is stable, has mass, is invisible, and has no charge, which fits precisely the characteristics of dark matter. Physicists believe the Earth moves in an invisible wind of dark matter that is probably passing through your body right now. If a photino collides with a proton, it may cause the proton to shatter into a shower of subatomic particles that can then be detected.

Born in 1821, Croll grew up poor, and his formal education lasted only to the age of thirteen. He worked at a variety of jobs—as a carpenter, insurance salesman, keeper of a temperance hotel—before taking a position as a janitor at Anderson’s (now the University of Strathclyde) in Glasgow. By somehow inducing his brother to do much of his work, he was able to pass many quiet evenings in the university library teaching himself physics, mechanics, astronomy, hydrostatics, and the other fashionable sciences of the day, and gradually began to produce a string of papers, with a particular emphasis on the motions of Earth and their effect on climate. Croll was the first to suggest that cyclical changes in the shape of Earth’s orbit, from elliptical (which is to say slightly oval) to nearly circular to elliptical again, might explain the onset and retreat of ice ages. No one had ever thought before to consider an astronomical explanation for variations in Earth’s weather. Thanks almost entirely to Croll’s persuasive theory, people in Britain began to become more responsive to the notion that at some former time parts of the Earth had been in the grip of ice. When his ingenuity and aptitude were recognized, Croll was given a job at the Geological Survey of Scotland and widely honored: he was made a fellow of the Royal Society in London and of the New York Academy of Science and given an honorary degree from the University of St. Andrews, among much else. Unfortunately,

To a theoretician, all these criticisms are troublesome but not fatal. But what does cause problems for a theoretician is that the model seems to predict a multiverse of parallel universes, many of which are crazier than those in the imagination of a Hollywood scriptwriter. String theory has an infinite number of solutions, each describing a perfectly well-behaved finite theory of gravity, which do not resemble our universe at all. In many of these parallel universes, the proton is not stable, so it would decay into a vast cloud of electrons and neutrinos. In these universes, complex matter as we know it (atoms and molecules) cannot exist. They only consist of a gas of subatomic particles. (Some might argue that these alternate universes are only mathematical possibilities and are not real. But the problem is that the theory lacks predictive power, since it cannot tell you which of these alternate universes is the real one.) This problem is actually not unique to string theory. For example, how many solutions are there to Newton’s or Maxwell’s equations? There are an infinite number, depending on what you are studying. If you start with a light bulb or a laser and you solve Maxwell’s equations, you find a unique solution for each instrument. So Maxwell’s or Newton’s theories also have an infinite number of solutions, depending on the initial conditions—that is, the situation you start with. This problem is likely to exist for any theory of everything. Any theory of everything will have an infinite number of solutions depending on the initial conditions. But how do you determine the initial conditions of the entire universe? This means you have to input the conditions of the Big Bang from the outside, by hand. To many physicists this seems like cheating. Ideally, you want the theory itself to tell you the conditions that gave rise to the Big Bang. You want the theory to tell you everything, including the temperature, density, and composition of the original Big Bang. A theory of everything should somehow contain its own initial conditions, all by itself. In other words, you want a unique prediction for the beginning of the universe. So string theory has an embarrassment of riches. Can it predict our universe? Yes. That is a sensational claim, the goal of physicists for almost a century. But can it predict just one universe? Probably not. This is called the landscape problem. There are several possible solutions to this problem, none of them widely accepted. The first is the anthropic principle, which says that our universe is special because we, as conscious beings, are here to discuss this question in the first place. In other words, there might be an infinite number of universes, but our universe is the one that has the conditions that make intelligent life possible. The initial conditions of the Big Bang are fixed at the beginning of time so that intelligent life can exist today. The other universes might have no conscious life in them.

Or think of the tale of the blind men who encounter an elephant for the first time. One wise man, touching the ear of the elephant, declares the elephant is flat and two-dimensional like a fan. Another wise man touches the tail and assumes the elephant is like rope or a one-dimensional string. Another, touching a leg, concludes the elephant is a three-dimensional drum or a cylinder. But actually, if we step back and rise into the third dimension, we can see the elephant as a three-dimensional animal. In the same way, the five different string theories are like the ear, tail, and leg, but we still have yet to reveal the full elephant, M-theory. Holographic Universe As we mentioned, with time new layers have been uncovered in string theory. Soon after M-theory was proposed in 1995, another astonishing discovery was made by Juan Maldacena in 1997. He jolted the entire physics community by showing something that was once considered impossible: that a supersymmetric Yang-Mills theory, which describes the behavior of subatomic particles in four dimensions, was dual, or mathematically equivalent, to a certain string theory in ten dimensions. This sent the physics world into a tizzy. By 2015, there were ten thousand papers that referred to this paper, making it by far the most influential paper in high-energy physics. (Symmetry and duality are related but different. Symmetry arises when we rearrange the components of a single equation and it remains the same. Duality arises when we show that two entirely different theories are actually mathematically equivalent. Remarkably, string theory has both of these highly nontrivial features.) As we saw, Maxwell’s equations have a duality between electric and magnetic fields—that is, the equations remain the same if we reverse the two fields, turning electric fields into magnetic fields. (We can see this mathematically, because the EM equations often contain terms like E2 + B2, which remain the same when we rotate the two fields into each other, like in the Pythagorean theorem). Similarly, there are five distinct string theories in ten dimensions, which can be proven to be dual to each other, so they are really a single eleven-dimensional M-theory in disguise. So remarkably, duality shows that two different theories are actually two aspects of the same theory. Maldacena, however, showed that there was yet another duality between strings in ten dimensions and Yang-Mills theory in four dimensions. This was a totally unexpected development but one that has profound implications. It meant that there were deep, unexpected connections between the gravitational force and the nuclear force defined in totally different dimensions. Usually, dualities can be found between strings in the same dimension. By rearranging the terms describing those strings, for example, we can often change one string theory into another. This creates a web of dualities between different string theories, all defined in the same dimension. But a duality between two objects defined in different dimensions was unheard of.