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23 FEBRUARY, 2015

This Idea Must Die: Some of the World’s Greatest Thinkers Each Select a Major Misconception Holding Us Back

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From the self to left brain vs. right brain to romantic love, a catalog of broken theories that hold us back from the conquest of Truth.

“To kill an error is as good a service as, and sometimes even better than, the establishing of a new truth or fact,” asserted Charles Darwin in one of the eleven rules for critical thinking known as Prospero’s Precepts. If science and human knowledge progress in leaps and bounds of ignorance, then the recognition of error and the transcendence of falsehood are the springboard for the leaps of progress. That’s the premise behind This Idea Must Die: Scientific Theories That Are Blocking Progress (public library) — a compendium of answers Edge founder John Brockman collected by posing his annual question“What scientific idea is ready for retirement?” — to 175 of the world’s greatest scientists, philosophers, and writers. Among them are Nobel laureates, MacArthur geniuses, and celebrated minds like theoretical physicist and mathematician Freeman Dyson, biological anthropologist Helen Fisher, cognitive scientist and linguist Steven Pinker, media theorist Douglas Rushkoff, philosopher Rebecca Newberger Goldstein, psychologist Howard Gardner, social scientist and technology scholar Sherry Turkle, actor and author Alan Alda, futurist and Wired founding editor Kevin Kelly, and novelist, essayist, and screenwriter Ian McEwan.

Brockman paints the backdrop for the inquiry:

Science advances by discovering new things and developing new ideas. Few truly new ideas are developed without abandoning old ones first. As theoretical physicist Max Planck (1858–1947) noted, “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.” In other words, science advances by a series of funerals.

Many of the answers are redundant — but this is a glorious feature rather than a bug of Brockman’s series, for its chief reward is precisely this cumulative effect of discerning the zeitgeist of ideas with which some of our era’s greatest minds are tussling in synchronicity. They point to such retirement-ready ideas as IQ, the self, race, the left brain vs. right brain divide, human nature and essentialism, free will, and even science itself. What emerges is the very thing Carl Sagan deemed vital to truth in his Baloney Detection Kit — a “substantive debate on the evidence by knowledgeable proponents of all points of view.”

Illustration by Lizi Boyd from 'Flashlight.' Click image for more.

One of the most profound undercurrents across the answers has to do with our relationship with knowledge, certainty, and science itself. And one of the most profound contributions in that regard comes from MacArthur fellow Rebecca Newberger Goldstein, a philosopher who thinks deeply and dimensionally about some of the most complex questions of existence. Assailing the idea that science makes philosophy obsolete — that science is the transformation of “philosophy’s vagaries into empirically testable theories” and philosophy merely the “cold-storage room in which questions are shelved until the sciences get around to handling them” — Goldstein writes:

The obsolescence of philosophy is often taken to be a consequence of science. After all, science has a history of repeatedly inheriting — and definitively answering — questions over which philosophers have futilely hemmed and hawed for unconscionable amounts of time.

The gravest problem with this theory, Goldstein notes, is its internal incoherence:

You can’t argue for science making philosophy obsolete without indulging in philosophical arguments… When pressed for an answer to the so-called demarcation problem, scientists almost automatically reach for the notion of “falsifiability” first proposed by Karl Popper. His profession? Philosophy. But whatever criterion you offer, its defense is going to implicate you in philosophy.

This is something that Dorion Sagan, Carl Sagan’s son, has previously addressed, but Goldstein brings to it unparalleled elegance of thought and eloquence of expression:

A triumphalist scientism needs philosophy to support itself. And the lesson here should be generalized. Philosophy is joined to science in reason’s project. Its mandate is to render our views and our attitudes maximally coherent.

In doing so, she argues, philosophy provides “the reasoning that science requires in order to claim its image as descriptive.” As a proponent of the vital difference between information and wisdom — the former being the material of science, the latter the product of philosophy, and knowledge the change agent that transmutes one into the other — I find the provocative genius of Goldstein’s conclusion enormously invigorating:

What idea should science retire? The idea of “science” itself. Let’s retire it in favor of the more inclusive “knowledge.”

Neuroscientist Sam Harris, author of the indispensable Spirituality Without Religion, echoes this by choosing our narrow definition of “science” as the idea to be put to rest:

Search your mind, or pay attention to the conversations you have with other people, and you’ll discover that there are no real boundaries between science and philosophy — or between those disciplines and any other that attempts to make valid claims about the world on the basis of evidence and logic. When such claims and their methods of verification admit of experiment and/or mathematical description, we tend to say our concerns are “scientific”; when they relate to matters more abstract, or to the consistency of our thinking itself, we often say we’re being “philosophical”; when we merely want to know how people behaved in the past, we dub our interests “historical” or “journalistic”; and when a person’s commitment to evidence and logic grows dangerously thin or simply snaps under the burden of fear, wishful thinking, tribalism, or ecstasy, we recognize that he’s being “religious.”

The boundaries between true intellectual disciplines are currently enforced by little more than university budgets and architecture… The real distinction we should care about — the observation of which is the sine qua non of the scientific attitude — is between demanding good reasons for what one believes and being satisfied with bad ones.

In a sentiment that calls to mind both Richard Feynman’s spectacular ode to a flower and Carl Sagan’s enduring wisdom on our search for meaning, Harris applies this model of knowledge to one of the great mysteries of science and philosophy — consciousness:

Even if one thinks the human mind is entirely the product of physics, the reality of consciousness becomes no less wondrous, and the difference between happiness and suffering no less important. Nor does such a view suggest that we’ll ever find the emergence of mind from matter fully intelligible; consciousness may always seem like a miracle. In philosophical circles, this is known as “the hard problem of consciousness” — some of us agree that this problem exists, some of us don’t. Should consciousness prove conceptually irreducible, remaining the mysterious ground for all we can conceivably experience or value, the rest of the scientific worldview would remain perfectly intact.

The remedy for all this confusion is simple: We must abandon the idea that science is distinct from the rest of human rationality. When you are adhering to the highest standards of logic and evidence, you are thinking scientifically. And when you’re not, you’re not.

Illustration from 'Once Upon an Alphabet' by Oliver Jeffers. Click image for more.

Psychologist Susan Blackmore, who studies this very problem — famously termed “the hard problem of consciousness” by philosopher David Chalmers in 1996 — benches the idea that there are neural correlates to consciousness. Tempting as it may be to interpret neural activity as the wellspring of that special something we call “consciousness” or “subjective experience,” as opposed to the “unconscious” rest of the brain, Blackmore admonishes that such dualism is past its cultural expiration date:

Dualist thinking comes naturally to us. We feel as though our conscious experiences were of a different order from the physical world. But this is the same intuition that leads to the hard problem seeming hard. It’s the same intuition that produces the philosopher’s zombie — a creature identical to me in every way except that it has no consciousness. It’s the same intuition that leads people to write, apparently unproblematically, about brain processes being either conscious or unconscious… Intuitively plausible as it is, this is a magic difference. Consciousness is not some weird and wonderful product of some brain processes but not others. Rather, it’s an illusion constructed by a clever brain and body in a complex social world. We can speak, think, refer to ourselves as agents, and so build up the false idea of a persisting self that has consciousness and free will.

Much of the allure of identifying such neural correlates of consciousness, Blackmore argues, lies in cultural mythologies rooted in fantasy rather than fact:

While people are awake they must always be conscious of something or other. And that leads along the slippery path to the idea that if we knew what to look for, we could peer inside someone’s brain and find out which processes were the conscious ones and which the unconscious ones. But this is all nonsense. All we’ll ever find are the neural correlates of thoughts, perceptions, memories, and the verbal and attentional processes that lead us to think we’re conscious.

When we finally have a better theory of consciousness to replace these popular delusions, we’ll see that there’s no hard problem, no magic difference, and no NCCs.

Illustration by Rob Hunter from 'A Graphic Cosmogony.' Click image for more.

In a related grievance, social psychologist Bruce Hood — author of the uncomfortable yet strangely comforting The Self Illusion — does away with the notion of the self. Half a century after Alan Watts enlisted Eastern philosophy in this mission, Hood presents a necessary integration of science and philosophy:

It seems almost redundant to call for the retirement of the free willing self, as the idea is neither scientific nor is this the first time the concept has been dismissed for lack of empirical support. The self did not have to be discovered; it’s the default assumption most of us experience, so it wasn’t really revealed by methods of scientific inquiry.

[…]

Yet the self, like a conceptual zombie, refuses to die. It crops up again and again in recent theories of decision making, as an entity with free will which can be depleted. It reappears as an interpreter in cognitive neuroscience, as able to integrate parallel streams of information arising from separable neural substrates. Even if these appearances of the self are understood to be convenient ways of discussing the emergent output of multiple parallel processes, students of the mind continue to implicitly endorse the idea that there’s a decision maker, an experiencer, a point of origin.

We know the self is constructed because it can be so easily deconstructed — through damage, disease, and drugs. It must be an emergent property of a parallel system processing input, output, and internal representations. It’s an illusion because it feels so real, but that experience is not what it seems. The same is true for free will. Although we can experience the mental anguish of making a decision… the choices and decisions we make are based on situations that impose on us. We don’t have the free will to choose the experiences that have shaped our decisions.

[…]

By abandoning the free willing self, we’re forced to reexamine the factors that are truly behind our thoughts and behavior and the way they interact, balance, override, and cancel out. Only then will we begin to make progress in understanding how we really operate.

Illustration by Ben Newman from 'A Graphic Cosmogony.' Click image for more.

Among the most provocative answers, in fact, is one examining the factors that underlie one of the most complex and seemingly human of our experiences: love. Biological anthropologist Helen Fisher, who studies the brain on love, points to romantic love and addiction as two concepts in need of serious reformulation and reframing — one best accomplished by understanding the intersection of the two. Fisher argues that we ought to broaden the definition of addiction and do away with science’s staunch notion that all addiction is harmful. Love, she argues with a wealth of neurobiological evidence in hand, is in fact a state that closely resembles that of addiction in terms of what happens in the brain during it — and yet love, anguishing as it may be at times, is universally recognized as the height of positive experience. In that respect, it presents a case of “positive addiction.” Fisher writes:

Love-besotted men and women show all the basic symptoms of addiction. Foremost, the lover is stiletto-focused on his/her drug of choice, the love object. The lover thinks obsessively about him or her (intrusive thinking), and often compulsively calls, writes, or stays in touch. Paramount in this experience is intense motivation to win one’s sweetheart, not unlike the substance abuser fixated on the drug. Impassioned lovers distort reality, change their priorities and daily habits to accommodate the beloved, experience personality changes (affect disturbance), and sometimes do inappropriate or risky things to impress this special other. Many are willing to sacrifice, even die for, “him” or “her.” The lover craves emotional and physical union with the beloved (dependence). And like addicts who suffer when they can’t get their drug, the lover suffers when apart from the beloved (separation anxiety). Adversity and social barriers even heighten this longing (frustration attraction).

In fact, besotted lovers express all four of the basic traits of addiction: craving, tolerance, withdrawal, and relapse. They feel a “rush” of exhilaration when they’re with their beloved (intoxication). As their tolerance builds, they seek to interact with the beloved more and more (intensification). If the love object breaks off the relationship, the lover experiences signs of drug withdrawal, including protest, crying spells, lethargy, anxiety, insomnia or hypersomnia, loss of appetite or binge eating, irritability, and loneliness. Lovers, like addicts, also often go to extremes, sometimes doing degrading or physically dangerous things to win back the beloved. And lovers relapse the way drug addicts do. Long after the relationship is over, events, people, places, songs, or other external cues associated with their abandoning sweetheart can trigger memories and renewed craving.

Fisher points to fMRI studies that have shown intense romantic love to trigger the brain’s reward system and the dopamine pathways responsible for “energy, focus, motivation, ecstasy, despair, and craving,” as well as the brain regions most closely associated with addiction and substance abuse. In shedding light on the neurochemical machinery of romantic love, Fisher argues, science reveals it to be a “profoundly powerful, natural, often positive addiction.”

Illustration by Christine Rösch from 'The Mathematics of Love.' Click image for more.

Astrophysicist Marcelo Gleiser, who has written beautifully about the necessary duality of knowledge and mystery, wants to do away with “the venerable notion of Unification.” He points out that smaller acts of unification and simplification are core to the scientific process — from the laws of thermodynamics to Newton’s law of universal gravity — but simplification as sweeping as reducing the world to a single Theory of Everything is misplaced:

The trouble starts when we take this idea too far and search for the Über-unification, the Theory of Everything, the arch-reductionist notion that all forces of nature are merely manifestations of a single force. This is the idea that needs to go.

Noting that at some point along the way, “math became equated with beauty and beauty with truth,” Gleiser writes:

The impulse to unify it all runs deep in the souls of mathematicians and theoretical physicists, from the Langlands program to superstring theory. But here’s the rub: Pure mathematics isn’t physics. The power of mathematics comes precisely from its detachment from physical reality. A mathematician can create any universe she wants and play all sorts of games with it. A physicist can’t; his job is to describe nature as we perceive it. Nevertheless, the unification game has been an integral part of physics since Galileo and has produced what it should: approximate unifications.

And yet this unification game, as integral as it may be to science, is also antithetical to it in the long run:

The scientific impulse to unify is crypto-religious… There’s something deeply appealing in equating all of nature to a single creative principle: To decipher the “mind of God” is to be special, is to answer to a higher calling. Pure mathematicians who believe in the reality of mathematical truths are monks of a secret order, open only to the initiated. In the case of high energy physics, all unification theories rely on sophisticated mathematics related to pure geometric structures: The belief is that nature’s ultimate code exists in the ethereal world of mathematical truths and that we can decipher it.

Echoing Richard Feynman’s spectacular commencement address admonishing against “cargo cult science,” Gleiser adds:

Recent experimental data has been devastating to such belief — no trace of supersymmetric particles, of extra dimensions, or of dark matter of any sort, all long-awaited signatures of unification physics. Maybe something will come up; to find, we must search. The trouble with unification in high energy physics is that you can always push it beyond the experimental range. “The Large Hadron Collider got to 7 TeV and found nothing? No problem! Who said nature should opt for the simplest versions of unification? Maybe it’s all happening at much higher energies, well beyond our reach.”

There’s nothing wrong with this kind of position. You can believe it until you die, and die happy. Or you can conclude that what we do best is construct approximate models of how nature works and that the symmetries we find are only descriptions of what really goes on. Perfection is too hard a burden to impose on nature.

People often see this kind of argument as defeatist, as coming from someone who got frustrated and gave up. (As in “He lost his faith.”) Big mistake. To search for simplicity is essential to what scientists do. It’s what I do. There are essential organizing principles in nature, and the laws we find are excellent ways to describe them. But the laws are many, not one. We’re successful pattern-seeking rational mammals. That alone is cause for celebration. However, let’s not confuse our descriptions and models with reality. We may hold perfection in our mind’s eye as a sort of ethereal muse. Meanwhile nature is out there doing its thing. That we manage to catch a glimpse of its inner workings is nothing short of wonderful. And that should be good enough.

Ceramic tile by Debbie Millman courtesy of the artist

Science writer Amanda Gefter takes issue with one particular manifestation of our propensity for oversimplification — the notion of the universe. She writes:

Physics has a time-honored tradition of laughing in the face of our most basic intuitions. Einstein’s relativity forced us to retire our notions of absolute space and time, while quantum mechanics forced us to retire our notions of pretty much everything else. Still, one stubborn idea has stood steadfast through it all: the universe.

[…]

In recent years, however, the concept of a single shared spacetime has sent physics spiraling into paradox. The first sign that something was amiss came from Stephen Hawking’s landmark work in the 1970s showing that black holes radiate and evaporate, disappearing from the universe and purportedly taking some quantum information with them. Quantum mechanics, however, is predicated upon the principle that information can never be lost.

Gefter points to recent breakthroughs in physics that produced one particularly puzzling such paradox, known as the “firewall paradox,” solved by the idea that spacetime is divided not by horizons but by the reference frames of the observers, “as if each observer had his or her own universe.”

But the solution isn’t a multiverse theory:

Yes, there are multiple observers, and yes, any observer’s universe is as good as any other’s. But if you want to stay on the right side of the laws of physics, you can talk only about one at a time. Which means, really, that only one exists at a time. It’s cosmic solipsism.

Here, psychology, philosophy, and cosmology converge, for what such theories suggest is what we already know about the human psyche — as I’ve put it elsewhere, the stories that we tell ourselves, whether they be false or true, are always real. Gefter concludes:

Adjusting our intuitions and adapting to the strange truths uncovered by physics is never easy. But we may just have to come around to the notion that there’s my universe and there’s your universe — but there’s no such thing as the universe.

Biological anthropologist Nina Jablonski points to the notion of race as urgently retirement-ready. Pointing out that it has always been a “vague and slippery concept,” she traces its origins to Hume and Kant — the first to divide humanity into geographic groupings called “races” — and the pseudoscientific seeds of racism this division planted:

Skin color, as the most noticeable racial characteristic, was associated with a nebulous assemblage of opinions and hearsay about the inherent natures of the various races. Skin color stood for morality, character, and the capacity for civilization; it became a meme.

Even though the atrocious “race science” that emerged in the 19th and early 20th century didn’t hold up — whenever scientists looked for actual sharp boundaries between groups, none came up — and race came to be something people identify themselves with as a shared category of experiences and social bonds, Jablonski argues that the toxic aftershocks of pseudoscience still poison culture:

Even after it has been shown that many diseases (adult-onset diabetes, alcoholism, high blood pressure, to name a few) show apparent racial patterns because people share similar environmental conditions, groupings by race are maintained. The use of racial self-categorization in epidemiological studies is defended and even encouraged. Medical studies of health disparities between “races” become meaningless when sufficient variables — such as differences in class, ethnic social practices, and attitudes — are taken into account.

Half a century after the ever-prescient Margaret Mead made the same point, Jablonski urges:

Race has a hold on history but no longer has a place in science. The sheer instability and potential for misinterpretation render race useless as a scientific concept. Inventing new vocabularies to deal with human diversity and inequity won’t be easy, but it must be done.

Psychologist Jonathan Gottschall, who has previously explored why storytelling is so central to the human experience, argues against the notion that there can be no science of art. With an eye to our civilization’s long struggle to define art, he writes:

We don’t even have a good definition, in truth, for what art is. In short, there’s nothing so central to human life that’s so incompletely understood.

Granted, Gottschall is only partly right, for there are some excellent definitions of art — take, for instance, Jeanette Winterson’s or Leo Tolstoy’s — but the fact that they don’t come from scientists only speaks to his larger point. He argues that rather than being unfit to shed light on the role of art in human life, science simply hasn’t applied itself to the problem adequately:

Scientific work in the humanities has mainly been scattered, preliminary, and desultory. It doesn’t constitute a research program.

If we want better answers to fundamental questions about art, science must jump into the game with both feet. Going it alone, humanities scholars can tell intriguing stories about the origins and significance of art, but they don’t have the tools to patiently winnow the field of competing ideas. That’s what the scientific method is for — separating the more accurate stories from the less accurate stories. But a strong science of art will require both the thick, granular expertise of humanities scholars and the clever hypothesis-testing of scientists. I’m not calling for a scientific takeover of the arts, I’m calling for a partnership.

[…]

The Delphic admonition “Know thyself” still rings out as the great prime directive of intellectual inquiry, and there will always be a gaping hole in human self-knowledge until we develop a science of art.

In a further testament to the zeitgeist-illuminating nature of the project, actor, author, and science-lover Alan Alda makes a passionate case for the same concept:

The trouble with truth is that not only is the notion of eternal, universal truth highly questionable, but simple, local truths are subject to refinement as well. Up is up and down is down, of course. Except under special circumstances. Is the North Pole up and the South Pole down? Is someone standing at one of the poles right-side up or upside-down? Kind of depends on your perspective.

When I studied how to think in school, I was taught that the first rule of logic was that a thing cannot both be and not be at the same time and in the same respect. That last note, “in the same respect,” says a lot. As soon as you change the frame of reference, you’ve changed the truthiness of a once immutable fact.

[…]

This is not to say that nothing is true or that everything is possible — just that it might not be so helpful for things to be known as true for all time, without a disclaimer… I wonder — and this is just a modest proposal — whether scientific truth should be identified in a way acknowledging that it’s something we know and understand for now, and in a certain way.

[…]

Facts, it seems to me, are workable units, useful in a given frame or context. They should be as exact and irrefutable as possible, tested by experiment to the fullest extent. When the frame changes, they don’t need to be discarded as untrue but respected as still useful within their domain. Most people who work with facts accept this, but I don’t think the public fully gets it.

That’s why I hope for more wariness about implying we know something to be true or false for all time and for everywhere in the cosmos.

Illustration from 'Once Upon an Alphabet' by Oliver Jeffers. Click image for more.

And indeed this elasticity of truth across time is at the heart of what I find to be the most beautiful and culturally essential contribution to the collection. As someone who believes that the stewardship of enduring ideas is at least as important as the genesis of new ones — not only because past ideas are the combinatorial building blocks of future ones but also because in order to move forward we always need a backdrop against which to paint the contrast of progress and improvement — I was most bewitched by writer Ian McEwan’s admonition against the arrogance of retiring any idea as an impediment to progress:

Beware of arrogance! Retire nothing! A great and rich scientific tradition should hang onto everything it has. Truth is not the only measure. There are ways of being wrong that help others to be right. Some are wrong, but brilliantly so. Some are wrong but contribute to method. Some are wrong but help found a discipline. Aristotle ranged over the whole of human knowledge and was wrong about much. But his invention of zoology alone was priceless. Would you cast him aside? You never know when you might need an old idea. It could rise again one day to enhance a perspective the present cannot imagine. It would not be available to us if it were fully retired.

To appreciate McEwan’s point, one need only look at something like Bertrand Russell’s timely thoughts on boredom, penned in 1930 and yet astoundingly resonant with our present anxieties about the societal side effects of current technology. McEwan captures this beautifully:

Every last serious and systematic speculation about the world deserves to be preserved. We need to remember how we got to where we are, and we’d like the future not to retire us. Science should look to literature and maintain a vibrant living history as a monument to ingenuity and persistence. We won’t retire Shakespeare. Nor should we Bacon.

Complement This Idea Must Die, the entirety of which weaves a mind-stretching mesh of complementary and contradictory perspectives on our relationship with knowledge, with some stimulating answers to previous editions of Brockman’s annual question, exploring the only thing worth worrying about (2013), the single most elegant theory of how the world works (2012), and the best way to make ourselves smarter (2011).

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18 FEBRUARY, 2015

What Mathematics Reveals About the Secret of Lasting Relationships and the Myth of Compromise

By:

Why 37% is the magic number, what alien civilizations have to do with your soul mate, and how to master the “negativity threshold” ideal for Happily Ever After.

In his sublime definition of love, playwright Tom Stoppard painted the grand achievement of our emotional lives as “knowledge of each other, not of the flesh but through the flesh, knowledge of self, the real him, the real her, in extremis, the mask slipped from the face.” But only in fairy tales and Hollywood movies does the mask slip off to reveal a perfect other. So how do we learn to discern between a love that is imperfect, as all meaningful real relationships are, and one that is insufficient, the price of which is repeated disappointment and inevitable heartbreak? Making this distinction is one of the greatest and most difficult arts of the human experience — and, it turns out, it can be greatly enhanced with a little bit of science.

That’s what mathematician Hannah Fry suggests in The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation (public library) — a slim but potent volume from TED Books, featuring gorgeous illustrations by German artist Christine Rösch. From the odds of finding your soul mate to how game theory reveals the best strategy for picking up a stranger in a bar to the equation that explains the conversation patterns of lasting relationships, Fry combines a humanist’s sensitivity to this universal longing with a scientist’s rigor to shed light, with neither sap nor cynicism, on the complex dynamics of romance and the besotting beauty of math itself.

She writes in the introduction:

Mathematics is ultimately the study of patterns — predicting phenomena from the weather to the growth of cities, revealing everything from the laws of the universe to the behavior of subatomic particles… Love — [like] most of life — is full of patterns: from the number of sexual partners we have in our lifetime to how we choose who to message on an internet dating website. These patterns twist and turn and warp and evolve just as love does, and are all patterns which mathematics is uniquely placed to describe.

[…]

Mathematics is the language of nature. It is the foundation stone upon which every major scientific and technological achievement of the modern era has been built. It is alive, and it is thriving.

In the first chapter, Fry explores the mathematical odds of finding your ideal mate — with far more heartening results than more jaundiced estimations have yielded. She points to a famous 2010 paper by mathematician and longtime singleton Peter Backus, who calculated that there are more intelligent extraterrestrial civilizations than eligible women for him on earth. Backus enlisted a formula known as the Drake equation — named after its creator, Frank Drake — which breaks down the question of how many possible alien civilizations there are into sub-estimates based on components like the average rate of star formation in our galaxy, the number of those stars with orbiting planets, the fraction of those planets capable of supporting life, and so forth. Fry explains:

Drake exploited a trick well known to scientists of breaking down the estimation by making lots of little educated guesses rather than one big one. The result of this trick is an estimate likely to be surprisingly close to the true answer, because the errors in each calculation tend to balance each other out along the way.

Scientists’ current estimate is that our galaxy contains around 10,000 intelligent alien civilizations — something we owe in large part to astronomer Jill Tarter’s decades-long dedication. Returning to Backus’s calculation, which yielded 26 eligible women on all of Earth, Fry notes that “being able to estimate quantities that you have no hope of verifying is an important skill for any scientist” — a technique known as a Fermi estimation, which is used in everything from job interviews to quantum mechanics — but suggests that his criteria might have been unreasonably stringent. (Backus based his formula, for instance, on the assumption that he’d find only 10% of the women he meets agreeable and only 5% attractive.)

In fact, this “price of admission” problem is also at the heart of a chapter probing the question of how you know your partner is “The One.” Fry writes:

As any mathematically minded person will tell you, it’s a fine balance between having the patience to wait for the right person and the foresight to cash in before all the good ones are taken.

Indeed, some such mathematically minded people have applied an area of mathematics known as “optimal stopping theory” to derive an actual equation that tells you precisely how many potential mates to reject before finding the perfect partner and helps you discern when it’s time to actually stop your looking and settle down with that person (P):

Fry explains:

It tells you that if you are destined to date ten people in your lifetime, you have the highest probability of finding The One when you reject your first four lovers (where you’d find them 39.87 percent of the time). If you are destined to date twenty people, you should reject the first eight (where Mister or Miz Right would be waiting for you 38.42 percent of the time). And, if you are destined to date an infinite number of partners, you should reject the first 37 percent, giving you just over a one in three chance of success.

[…]

Say you start dating when you are fifteen years old and would ideally like to settle down by the time you’re forty. In the first 37 percent of your dating window (until just after your twenty-fourth birthday), you should reject everyone; use this time to get a feel for the market and a realistic expectation of what you can expect in a life partner. Once this rejection phase has passed, pick the next person who comes along who is better than everyone who you have met before. Following this strategy will definitely give you the best possible chance of finding the number one partner on your imaginary list.

This formula, it turns out, is a cross-purpose antidote to FOMO, applicable to various situations when you need to know when to stop looking for a better option:

Have three months to find somewhere to live? Reject everything in the first month and then pick the next house that comes along that is your favorite so far. Hiring an assistant? Reject the first 37 percent of candidates and then give the job to the next one who you prefer above all others. In fact, the search for an assistant is the most famous formulation of this theory, and the method is often known as the “secretary problem.”

But the most interesting and pause-giving chapter is the final one, which brings modern lucidity to the fairy-tale myth that “happily ever after” ensues unabated after you’ve identified “The One,” stopped your search, and settled down him or her. Most of us don’t need a scientist to tell us that “happily ever after” is not a destination or a final outcome but a journey and an active process in any healthy relationship. Fry, however, offers some enormously heartening and assuring empirical findings, based on a fascinating collaboration between mathematicians and psychologists, confirming this life-tested and often hard-earned intuitive understanding.

Fry examines what psychologists studying longtime couples have found about the key to successful relationships:

Every relationship will have conflict, but most psychologists now agree that the way couples argue can differ substantially, and can work as a useful predictor of longer-term happiness within a couple.

In relationships where both partners consider themselves as happy, bad behavior is dismissed as unusual: “He’s under a lot of stress at the moment,” or “No wonder she’s grumpy, she hasn’t had a lot of sleep lately.” Couples in this enviable state will have a deep-seated positive view of their partner, which is only reinforced by any positive behavior: “These flowers are lovely. He’s always so nice to me,” or “She’s just such a nice person, no wonder she did that.”

In negative relationships, however, the situation is reversed. Bad behavior is considered the norm: “He’s always like that,” or “Yet again. She’s just showing how selfish she is.” Instead, it’s the positive behavior that is considered unusual: “He’s only showing off because he got a pay raise at work. It won’t last,” or “Typical. She’s doing this because she wants something.

She cites the work of psychologist John Gottman, who studies why marriages succeed or fail. He spent decades observing how couples interact, coding and measuring everything from their skin conductivity to their facial expressions, and eventually developed the Specific Affect Coding System — a method of scoring how positive or negative the exchanges are. But it wasn’t until Gottman met mathematician James Murray and integrated his mathematical models into the system that he began to crack the code of why these toxic negativity spirals develop. (Curiously, these equations have also been used to understand what happens between two countries during war — a fact on which Fry remarks that “an arguing couple spiraling into negativity and teetering on the brink of divorce is actually mathematically equivalent to the beginning of a nuclear war.”)

Fry presents the elegant formulae the researchers developed for explaining these patterns of human behavior. (Although the symbols stand for “wife” and “husband,” Fry notes that Murray’s models don’t factor in any stereotypes and are thus equally applicable to relationships across all orientations and gender identities.)

She breaks down the equations:

The left-hand side of the equation is simply how positive or negative the wife will be in the next thing that she says. Her reaction will depend on her mood in general (w), her mood when she’s with her husband (rwWt), and, crucially, the influence that her husband’s actions will have on her (IHM). The Ht in parentheses at the end of the equation is mathematical shorthand for saying that this influence depends on what the husband has just done.

The equations for the husband follow the same pattern: h, rHHt, and IHM are his mood when he’s on his own, his mood when he’s with his wife, and the influence his wife has on his next reaction, respectively.

The researchers then plotted the effects the two partners have on each other — empirical evidence for Leo Buscaglia’s timelessly beautiful notion that love is a “dynamic interaction”:

In this version of the graph, the dotted line indicates that the husband is having a positive impact on his wife. If it dips below zero, the wife is more likely to be negative in her next turn in the conversation.

What all of this translates into is actually strikingly similar to Lewis Carroll’s advice on resolving conflict in correspondence. “If your friend makes a severe remark, either leave it unnoticed, or make your reply distinctly less severe,” Carroll counseled, adding “and if he makes a friendly remark, tending towards ‘making up’ the little difference that has arisen between you, let your reply be distinctly more friendly.” Carroll was a man of great psychological prescience in many ways, and this particular insight is paralleled by Gottman and Murray’s findings, which Fry summarizes elegantly:

Imagine that the husband does something that is a little bit positive: He could agree with her last point, or inject a little humor into their conversation. This action will have a small positive impact on the wife and make her more likely to respond with something positive, too… [But] if the husband is a little bit negative — like interrupting her while she is speaking — he will have a fixed and negative impact on his partner. It’s worth noting that the magnitude of this negative influence is bigger than the equivalent positive jump if he’s just a tiny bit positive. Gottman and his team deliberately built in this asymmetry after observing it in couples in their study.

And here is the crucial finding — T- is the point known as a negativity threshold, at which the husband’s negative effect becomes so great that it renders the wife unwilling to diffuse the situation with positivity and she instead responds with more negativity. This is how the negativity spirals are set off. But the most revelatory part is what this suggests about the myth of compromise.

As Fry points out, it makes sense to suppose that the best strategy is to aim for a high negativity threshold — “a relationship where you give your partner room to be themselves and only bring up an issue if it becomes a really big deal.” And yet the researchers found the opposite was true:

The most successful relationships are the ones with a really low negativity threshold. In those relationships, couples allow each other to complain, and work together to constantly repair the tiny issues between them. In such a case, couples don’t bottle up their feelings, and little things don’t end up being blown completely out of proportion.

She adds the important caveat that a healthy relationship isn’t merely one in which both partners are comfortable complaining but also one in which the language of those complaints doesn’t cast the complainer as a victim of the other person’s behavior.

In the remainder of The Mathematics of Love, Fry goes on to explore everything from the falsehoods behind the standard ideals of beauty to the science of why continually risking rejection is a sounder strategy for success in love (as in life) than waiting for a guaranteed outcome before trying, illustrating how math’s power to abstract reality invites greater understanding of our most concrete human complexities and our deepest yearnings.

Complement it with a fascinating look at what troves of online dating data reveal about being extraordinary, Dan Savage on the myth of “The One,” and Adrienne Rich on how relationships define our truths.

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13 FEBRUARY, 2015

Mozart’s Magnificent Love Letter to His Wife

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“If people could see into my heart I should almost feel ashamed.”

It’s hardly surprising that humanity’s most beautiful minds — the creative visionaries who bequeath us with the finest works of art, music, and literature — should also be the ones who author the most bewitching love letters, that highest form of what Virginia Woolf called “the humane art.” One particularly heartwarming specimen of the genre comes from Wolfgang Amadeus Mozart (January 27, 1756–December 5, 1791) — doubly so for the unusual start of the romance that would become the love of his life.

In late 1777, Mozart fell in love with Aloysia Weber — one of four daughters in a highly musical family. Despite the early cultivation of his talent, he was only just beginning to find self-actualization; she, on the other hand, was already a highly successful singer. (A century later, another great composer — Tchaikovsky — would tussle with the same challenge.) Despite her initial interest, Aloysia ultimately rejected his advances.

Over the next few years, Mozart established himself not only as the finest keyboard player in Vienna, but also as a promising young composer. When the father of the family died in 1782, the Webers began renting their house to lodgers to make ends meet. Young Mozart moved in, and soon fell in love with Constanze — the third Weber daughter.

On August 4, 1782, the two were married and remained together, very much in love, until Mozart’s death nine years later.

Shortly before his sudden death, in a letter from September of 1790 found in Love Letters of Great Men (public library) — a collection of romantic correspondence featuring Lord Byron, F. Scott Fitzgerald, James Joyce, Voltaire, Leo Tolstoy, and dozens more lovers of letters — Mozart writes to Constanze from Frankfurt, where he had gone seeking gainful employment to remedy the family’s financial downturn:

Dearest little Wife of my heart!

If only I had a letter from you, everything would be all right…

Dearest, I have no doubt that I shall get something going here, but it won’t be easy as you and some of our friends think. — It is true, I am known and respected here; but, well — No — let us just see what happens. — In any case, I do prefer to play it safe, that why I would like to conclude this deal with H… because I would get some money into my possession without having to pay any out; all I would have to do then is work, and I shall be only too happy to do that for my little wife.

After a getting a few more practical matters out of the way, Mozart fully surrenders to the poetical:

I get all excited like a child when I think about being with you again — If people could see into my heart I should almost feel ashamed. Everything is cold to me — ice-cold. — If you were here with me, maybe I would find the courtesies people are showing me more enjoyable, — but as it is, it’s all so empty — adieu — my dear — I am Forever

your Mozart who loves you
with his entire soul.

But even lovelier than the signature is the part that comes after it. Mozart violates in the most endearing of ways Lewis Carroll’s rule about postscript and writes:

PS. — while I was writing the last page, tear after tear fell on the paper. But I must cheer up — catch — An astonishing number of kisses are flying about — The deuce! — I see a whole crowd of them. Ha! Ha!… I have just caught three — They are delicious… I kiss you millions of times.

Complement this gem from Love Letters of Great Men with other masterworks of the genre, including the exquisite letters of Vladimir Nabokov to his wife Véra, Violet Trefusis to Vita Sackville-West, Vita Sackville-West to Virginia Woolf, Frida Kahlo to Diego Rivera, Oscar Wilde to Bosie, and Franz Kafka to Felice Bauer.

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12 FEBRUARY, 2015

The Missing Piece Meets the Big O: Shel Silverstein’s Sweet Allegory for the Simple Secret of Love and the Key to Nurturing Relationships

By:

A gentle reminder that the best relationships don’t complete us but let us grow and become more fully ourselves.

The best children’s books, as Tolkien asserted and Sendak agreed, aren’t written for children; they are enjoyed by children, but they speak to our deepest longings and fears, and thus enchant humans of all ages. But the spell only works, as legendary children’s book editor Ursula Nordstrom memorably remarked, “if the dull adult isn’t too dull to admit that he doesn’t know the answers to everything.”

Few storytellers have immunized us against our adult dullness, generation after generation, more potently than Shel Silverstein, one of the many beloved authors and artists — alongside Maurice Sendak, E.B. White, Margaret Wise Brown, and dozens of others — whose genius Nordstrom cultivated under her compassionate and creatively uncompromising wing. In a letter from September of 1975, she wrote: “Shel promised me that it was in really good and almost final shape… I hope with all my heart that this is really the case.” Silverstein had gone to visit Nordstrom some weeks earlier and recited the story for her, which she found to be “very very good (in fact terrific).” “I hope he hasn’t messed it up,” she adds in the letter, “and I’m pretty sure he hasn’t.” Nordstrom’s intuition and her unflinching faith in her authors and artists was never misplaced.

In 1976, The Missing Piece Meets the Big O (public library) was published — a minimalist, maximally wonderful allegory at the heart of which is the emboldening message that true love doesn’t complete us, even though at first it might appear to do that, but lets us grow and helps us become more fully ourselves. It’s a story especially poignant for those of us who have ever suffered from Savior Syndrome or Victim Syndrome and sought a partner to either fix or be fixed by, the result of which is often disastrous, always disappointing, and never salvation or true love.

Silverstein tells the tale of a lonely little wedge that dreams of finding a big circle into which it can fit, so that together they can roll and go somewhere. Various shapes come by, but none are quite right.

In these unbefitting rolling partners, one can’t help but recognize the archetypes implicated in failed friendships and romances — there are the damaged-beyond-repair (“some had too many pieces missing”), the overly complicated (“some had too many pieces, period”) the worshipper (“one put it on a pedestal and left it there”), the self-involved narcissist (“some rolled by without noticing”).

The missing piece tries to make itself more attractive, flashier — but that scares away the shy ones and leaves it ever lonelier.

At last, one comes along that fits just right, and the two roll on by blissfully.

But then, something strange starts happening — the missing piece begins to grow.

And just like in any relationship where one partner grows and the other remains static, things end in disappointment — and then they just end. The static circle moves along, looking for a piece that won’t grow.

At last, a shape comes by that looks completely different — it has no piece missing at all — and introduces itself as the Big O.

The exchange between the missing piece and the Big O is nothing short of breathstopping:

“I think you are the one I have been waiting for,” said the missing piece. “Maybe I am your missing piece.”

“But I am not missing a piece,” said the Big O. “There is no place you would fit.”

“That is too bad,” said the missing piece. “I was hoping that perhaps I could roll with you…”

“You cannot roll with me,” said the Big O, “but perhaps you can roll by yourself.”

This notion is utterly revelatory for the missing piece, doubly so when the Big O asks if it has ever tried. “But I have sharp corners,” the missing piece offers half-incredulously, half-defensively. “I am not shaped for rolling.”

But corners, the Big O assures it, can wear off — another elegant metaphor for the self-refinement necessary in our personal growth. With that, the Big O rolls off, leaving the missing piece alone once more — but, this time, with an enlivening idea to contemplate.

The missing piece goes “liftpullflopliftpullflop” forward, over and over, until its edges begin to wear off and its shape starts to change. Gradually, it begins to bounce instead of bump and then roll instead of bounce — rolling, like it always dreamt of doing with the aid of another, only all by itself.

And here comes Silverstein’s tenderest, most invigorating magic — when the missing piece becomes its well-rounded self, the Big O emerges, silently and without explanation. In the final scene, the two are seen rolling side by side, calling to mind Antoine de Saint-Exupéry’s contribution to history’s greatest definitions of love: “Love does not consist of gazing at each other, but in looking outward together in the same direction.”

The Missing Piece Meets the Big O is immeasurably wonderful in a way to which neither text nor pixel does any justice. Complement it with Wednesday, another minimalist and wholly wordless allegory for friendship, and Norton Juster’s vintage masterwork of poetic geometry, The Dot and the Line: A Romance in Lower Mathematics, then treat yourself to this animated adaptation of Silverstein’s The Giving Tree and his touching duet with Johnny Cash.

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