Edge - Scientific Concepts

Reynolds Number

"The internal motion of water assumes one or other of two broadly distinguishable forms," Osborne Reynolds reported to the Royal Society in 1883. "Either the elements of the fluid follow one another along lines of motion which lead in the most direct manner to their destination, or they eddy about in sinuous paths the most indirect possible." Reynolds puzzled over how to define the point at which a moving fluid (or a fluid with an object moving through it) makes the transition from stable to unstable flow. He noted that the transition depends on the ratio between inertial forces (characterized by mass, distance, and velocity) and viscous forces (characterized by the "stickiness" of the fluid). When this ratio, now termed the Reynolds number, reaches a certain critical value, the fluid shifts from orderly, deterministic behavior to disorderly, probabilistic behavior resistant to description in full detail. The two regimes are known as laminar and turbulent flow. The Reynolds number is...

The Texas Sharpshooter

A city-slicker statistician was driving through the backwoods of rural Texas, so the story goes, when she slammed on the brakes. There, right by the side of the road, was a barn that bore witness to a nigh-impossible feat of marksmanship. The barn was covered with hundreds of neat little white bullseyes, each of which was perforated with a single bullet hole in the dead center. The incredulous statistician got out of the car and examined the barn, muttering about Gaussian distributions and probability density functions. She didn't even notice that Old Joe had sidled up to her, ancient Winchester slung over his shoulder. Joe cleared his throat. With a start, the statistician looked at Joe with amazement. "Four hundred and twelve targets, every single one of which is hit in the center with less than 2 percent deviation every time... the odds against that are astronomical! You must be the most accurate rifleman in history. How do you do it?" Without a word, Joe walked ten paces away from ...

The Transcriptome

A few months ago I sequenced my genes. It is a 700 Megabyte text file that looks something like this: AGCCCCTCAGGAGTCCGGCCACATGGAAACTCCTCATTCCGGAGGTCAGTCAGATTTACCCTTGAGTTCAAACTTCAGGGTCCAGAGGCTGATAATCTACTTACCCAAACATAGGGCTCACCTTGGCGTCGCGTCCGGCGGCAAACTAAGAACACGTCGTCTAAATGACTTCTTAAAGTAGAATAGCGTGTTCTCTCCTTCCAGCCTCCGAAAAACTCGGACCAAAGATCAGGCTTGTCCGTTCTTCGCTAGTGATGAGACTGCGCCTCTGTTCGTACAACCAATTTAGG Each individual A, C, G and T are organic molecules that form the building blocks of what makes me "me": my DNA. It is approximately 3.3 billion pairs of nucleotides organized in around 24 thousand genes. The information of every living being is codified in this manner. Our shape, our capacities, abilities, needs and even predisposition to disease are determined largely by our genes. But this information is only a small percentage (less than 2%) of what can be found in the DNA that each of the cells of my body carry. That is the percentage of the DNA that encodes proteins, the molecules that carry ...

Type I and Type II Errors

A few years ago, a reporter at a leading financial daily called with an intriguing question: "We're doing a story about decision making, and asking researchers whether they follow their own advice." I must have chuckled because she continued: "I just talked with one man who said, 'For heaven's sake, you don't think I actually use this stuff, do you? My decisions are as bad as everyone else's!'" I suspect my colleague was being ironic, or perhaps tweaking the reporter. I gave a few examples I have found useful—sunk cost fallacy, regression toward the mean, and more—but then focused on one concept that everyone should understand: Type I and Type II errors, or false positives and false negatives. The basic idea is straightforward: We should want to go ahead with a course of action when it will succeed and refrain when it will fail; accept a hypothesis when it is true and reject when it is false; convict a defendant who is guilty and free one who is innocent. Naturally, we spend time and e...

Alternative Possibilities

At the heart of scientific thinking is the systematic evaluation of alternative possibilities. The idea is so foundational that it's woven into the practice of science itself. Consider a few examples. Statistical hypothesis testing is all about ruling out alternatives. With a null hypothesis test, one evaluates the possibility that a result was due to chance alone. Randomized controlled trials, the gold standard for drawing causal conclusions, are powerful precisely because they rule out alternatives: they diminish the plausibility of alternative explanations for a correlation between treatment and effect. And in science classes and laboratories across the globe, students are trained to generate alternative explanations for every observation—an exercise that peer reviewers take on as a professional obligation. The systematic evaluation of alternative possibilities has deep roots in the origins of science. In the 17th century, Francis Bacon wrote about the special role of instanti...

Epigenetics

Epigenetics is a term that has been around for more than a century, but its usage in the public domain has increased markedly in recent years. In the last decade or so there have been dozens of articles in newspapers (notably the New York Times) and magazines, such as the New Yorker, devoted to this topic. Yet when I queried ten people working in the research office of a major university, only one had a general sense of what the term meant, stating that it deals with "how experience influences genes." Close enough, but the other nine had no idea, despite the fact that all were college graduates, two were lawyers and four others had graduate degrees. Not satisfied by the results of this unscientific sample, I asked an associate dean of a leading medical school how many first-year medical students knew the meaning of this term. He guessed that the majority would know, but at a subsequent lecture when he did a polling of fifty students, only about a dozen could provide a cogent definition...

Coalitional Instincts

Every human—not excepting scientists—bears the whole stamp of the human condition. This includes evolved neural programs specialized for navigating the world of coalitions—teams, not groups. (Although the concept of coalitional instincts has emerged over recent decades, there is no mutually agreed term for this concept yet.) These programs enable us and induce us to form, maintain, join, support, recognize, defend, defect from, factionalize, exploit, resist, subordinate, distrust, dislike, oppose, and attack coalitions. Coalitions are sets of individuals interpreted by their members and/or by others as sharing a common abstract identity (including propensities to act as a unit, to defend joint interests, and to have shared mental states and other properties of a single human agent, such as status and prerogatives). Why do we see the world this way? Most species do not and cannot: Even those that have linear hierarchies do not: Among elephant seals, for example, an alpha can reproduct...

Relative Information

Everybody knows what "information" is. It is the stuff that overabounds online; which you ask the airport kiosk when you don't know how to get downtown; or which is stored in your USB sticks. It carries meaning. Meaning is interpreted in our head, of course. So, is there anything out there which is just physical, independent from our head, which is information? Yes. It is called "relative information." In nature, variables are not independent; for instance, in any magnet, the two ends have opposite polarities. Knowing one amounts to knowing the other. So we can say that each end "has information" about the other. There is nothing mental in this; it is just a way of saying that there is a necessary relation between the polarities of the two ends. We say that there is "relative information" between two systems anytime the state of one is constrained by the state of the other. In this precise sense, physical systems may be said to have information about one another, with no need for a mi...

Parallel Universes of Quantum Mechanics

In 1957, a Princeton physics graduate student named Hugh Everett showed that the consistency of quantum mechanics required the existence of an infinity of universes parallel to our universe. That is, there has to be a person identical to you reading this identical article right now in a universe identical to ours. Further, there have to be an infinite number of universes, and thus an infinite number of people identical to you in them. Most physicists, at least most physicists who apply quantum mechanics to cosmology, accept Everett's argument. So obvious is Everett's proof for the existence of these parallel universes, that Steve Hawking once told me that he considered the existence of these parallel universes "trivially true." Everett's insight is the greatest expansion of reality since Copernicus showed us that our star was just one of many. Yet few people have even heard of the parallel universes, or thought about the philosophical and ethical implications of their existence. Kepler...

The Longevity Factor

In 1977 the Voyager probes were launched toward the outer Solar System, each carrying a Golden Record containing hundreds of sounds and images, from the cry of a newborn baby to the music of Beethoven. In the emptiness of space, they could last for millions of years. By that time, will they be the sole representatives of human culture in the cosmos? Or primitive relics of a civilization that has since bloomed to the galactic scale? The Drake equation estimates the number of currently communicative civilizations in the Milky Way, by multiplying a series of terms, such as the fraction of stars with planets and the fraction of inhabited planets on which intelligence evolves. The final term in the equation does not get much attention. Yet it is crucial not just for the question of intelligent life, but for the question of how to live intelligently. This is L, the "Longevity Factor," and it represents the average lifespan of a technological civilization. What determines this average? Surely...

Criticality

In physics we say a system is in a critical state when it is ripe for a phase transition. Consider water turning into ice, or a cloud that is pregnant with rain. Both of these are examples of physical systems in a critical state. The dynamics of criticality, however, are not very intuitive. Consider the abruptness of freezing water. For an outside observer, there is no difference between cold water and water that is just about to freeze. This is because water that is just about to freeze is still liquid. Yet, microscopically, cold water and water that is about to freeze are not the same. When close to freezing, water is populated by gazillions of tiny ice crystals, crystals that are so small that water remains liquid. But this is water in a critical state, a state in which any additional freezing will result in these crystals touching each other, generating the solid mesh we know as ice. Yet, the ice crystals that formed during the transition are infinitesimal. They are just the last ...

State

In physics, math, and computer science, the state of a system is an encapsulation of all the information you'd ever need to predict what it will do, or at least its probabilities to do one thing versus another, in response to any possible prodding of it. In a sense, then, the state is a system's "hidden reality," which determines its behavior beneath surface appearances. But in another sense, there's nothing hidden about a state—for any part of the state that never mattered for observations could be sliced off with Occam's Razor, to yield a simpler and better description. When put that way, the notion of "state" seems obvious. So then why did Einstein, Turing, and others struggle for years with the notion, along the way to some of humankind's hardest-won intellectual triumphs? Consider a few puzzles: The puzzle about the computer is a stand-in for countless debates I've gotten into with non-scientist intellectuals. The resolution, I think, is to specify a state for the computer, involv...

Abstraction

Open up Ada Lovelace's 1843 paper about Charles Babbage's unbuilt Analytical Engine, and, if you are geek enough, and can cope with long 19th-century sentences, it is astonishingly readable today. The Analytical Engine was entirely mechanical. Setting a heavy metal disc with ten teeth stored a digit, a stack of fifty such discs stored a fifty-digit number, and the store, or memory, would have contained 100 such stacks. A basic instruction to add two numbers moved them from the store to the mill, or CPU, where they would be added together, and moved back to a new place in the store to await further use: all mechanically. It was to be programmed with punched cards, representing variables and operations, with further elaborate mechanisms to move the cards around, and reuse groups of them when loops were needed. Babbage estimated that his gigantic machine would take three minutes to multiply two twenty-digit numbers. The paper is so readable because Lovelace describes the machine, not in t...

The Breeder's Equation

R = h2 S. R is the response to selection, S is the selection differential, and h2 is the narrow-sense heritability. This is the workhorse equation for quantitative genetics. The selective differential S, is the difference between the population average and the average of the parental population (some subset of the total population). Almost everything is moderately to highly heritable, from height and weight to psychological traits. Consider IQ. Imagine a set of parents with IQs of 120, drawn from a population with an average IQ of 100. Suppose that the narrow-sense heritability of IQ (in that population, in that environment) is 0.5. The average IQ of their children will be 110. That's what is usually called regression to the mean. Do the same thing with a population whose average IQ is 85. We again choose parents with IQs of 120, and the narrow-sense heritability is still 0.5. The average IQ of their children will be 102.5—they regress to a lower mean. You can think of it this way. In ...

The Gaia Hypothesis

According to James Lovelock's Gaia Hypothesis, the planet Earth is a self-regulated living being. In this captivating theory, the planet, in all its parts, remains in suitable conditions for life thanks to the behavior and action of living organisms. Lovelock is an independent scientist, environmentalist, inventor, author and researcher whose early interest in science fiction led him to Olaf Stapledon's idea that the Earth itself may have consciousness. From Erwin Schrödinger's What Is Life, he picked up the theory of "order-from-disorder," based on the second law of thermodynamics, according to which "entropy only increases in a closed system (such as the universe)" and thus "living matter evades the decay to thermodynamical equilibrium by homeostatically maintaining negative entropy ... in an open system." As a researcher at NASA, he worked on developing instruments for the analysis of extraterrestrial atmospheres. This led to an interest in potential life forms on Mars. He came up w...

Reflective Beliefs

Do Christians believe that God is omniscient in the same way that they believe there's a table in the middle of their living room? On the one hand, we can refer to both attitudes using the same term—belief—and Christians would readily assent to both. On the other hand, these two beliefs behave markedly differently. The belief about the living room table is, so to speak, free to roam around our minds, guiding behavior (we must go around the table, we can put dishes on it) and our inferences (a child might use it as a hiding place, its size limits how many guests we can have for dinner). By contrast, the belief about God's omniscience seems more constrained. It guides some behaviors—for instance verbal behavior when quizzed on the subject—but not others. Believers in God's omniscience might still try to hide actions or thoughts from God. They sometimes try to attract his attention. Believers in God's omnipotence may still imagine God attending to prayers one after the other. That people ...

Boolean Logic

George Boole, the son of a shoemaker, left school at sixteen, and ended up a Professor of Mathematics at Queens College in Cork in Ireland. As the only breadwinner in his family, he became a teacher at age sixteen, opened his own school in Lincoln in England by age nineteen, and fifteen years later was a mathematician and philosopher of logic. Why did Google celebrate his 200th birthday on the 2nd November 2015? And why should we remember his contributions? In 1854 he wrote a book called An Investigation of the Laws of Thought which distilled the essence of logical thought down to terms like AND (e.g., x AND y), OR (e.g., x OR y), and NOT (e.g., NOT x), or combinations of these. This took Aristotelian logic (the syllogism, expressed in words) and insisted these be formulated as equations, which was a revolutionary step. Equally important, Boolean logic is today seen as the foundations of the "information age," or what we also call the "computer age." This is because each "value" in the...

Optimization

Lawns in public places all suffer from the same problem: People don't like detours. Throughout the world we search for the fastest route, the closest parking spot, the shortest way to the restroom—we optimize. Incremental modification, followed by evaluation and readjustment, guides us to solutions that maximize a desired criterion. These little series of trial and error are so ingrained we rarely think about them. But optimization, once expressed in scientific terms, is one of the most versatile scientific concepts we know. Optimization under variation isn't only a human strategy but a ubiquitous selection principle that you can observe everywhere in nature. A soap bubble minimizes surface area. Lightning uses the way of least resistance. Light travels the path which takes the least amount of time. And with only two slight twists, optimization can be applied even more widely. The first twist is that many natural systems don't actually perform the modifications—they work by what physic...

Spatial Agency Bias

Progressive, dynamic and forward-thinking—these are personal qualities that are highly sought after in practically all social circles and cultures. Do you want to be seen in such positive terms whenever people come across your picture? An intriguing line of psychological research suggests how to accomplish just that: When caught on film you need to pay attention to the direction in which you are facing. People who look toward the right are perceived as more powerful and agentic than those who point to the left. In other words, how a person is represented in space shapes perceivers' automatic impressions, as if we imagine the depicted person as literally moving from left to right, along an imaginary path that takes them from the present to future accomplishments. This principle of "spatial agency bias" includes how simple actions are interpreted. For example, a soccer goal is considered to be more elegant, and an act of aggression to be more forceful when the actor moves from left to ri...

Invariance

Science is supposed to be about an objective world. Yet our observations are inherently subjective, made from a particular frame of reference, point of view. How do we get beyond this subjectivity to see the world as it truly is? Through the idea of invariance. To have a chance of being objective, our theory of the world must at least be intersubjectively valid: It must take the same form for all observers, regardless of where they happen to be located, or when they happen to be doing their experiment, or how they happen to be moving, or how their lab happens to be oriented in space (or whether they are male or female, or Martian or Earthling, or...). Only by comparing observations from all possible perspectives can we distinguish what is real from what is mere appearance or projection. Invariance is an idea of enormous power. In mathematics, it gives rise to the beauties of group theory and Galois theory, since the shifts in perspective that leave something invariant form an alg...

Ansatz

"Ansatz" is a fancy way to say that scientists make stuff up. The most common formulation of physics is based on what are called differential equations, which are formulas that relate the rate at which things change. Some of these are easy to solve, some are hard to solve, and some can't be solved. It turns out that there's a deep reason why there's no universal way to find these solutions, because if that existed it would let you answer questions that we know to be uncomputable (thanks to Alan Turing). But differential equations do have a very handy property: their solutions are unique. That means that if you find a solution, it's the solution. You can guess a solution, try it out, and fiddle with it to see if you can make it work. If it does, your guess is justified after the fact. That's what an ansatz is, a guess that you test. It's a German word that could be translated as initial placement, starting point, approach, or attempt. Hans Bethe famously did this in 1931 with an ansatz ...

Impedance Matching

"Impedance" is a measure of how a system resists the inflow of energy. Often, a system can be changed to accept energy more efficiently, by adding an element called an "impedance matcher." Most people have never heard of an impedance matcher, but once you know about them, you begin to see them everywhere: in the shape of a trumpet, the anti-reflective coating on a lens, and the foam spikes on the inside of a recording booth. A familiar example of an impedance matcher is the transmission of an automobile, which couples the energy from the engine into the wheels by converting the relatively fast rotation of the engine into the slower, stronger rotation required to propel the car. The transformer on an electric pole solves an analogous problem, converting the high-voltage electricity on the transmission lines to the high-current electricity required to power your home. Lots of machines, from jet engines to radios, depend on impedance matchers to move energy from one part of the system to ...

Indexical Information

"Information" is a term with many meanings, but in physics or information theory we can quantify information as the specificity of a subset of many possibilities. Consider an 8-digit binary string like 00101010. There are 256 such strings, but if we specify that the first digit is "0" we define a subset of 128 strings with that property; this reduction corresponds (via a base-2 logarithm in the formula) to one bit of information. The string 00101010, one out of 256, has 8 bits of information. This information, which is created by pointing to particular instances out of many possibilities, can be called indexical information. (A closely related concept is statistical information, in which each possibility is assigned a probability.) This notion of information has interesting implications. You might imagine that combining many strings like 00101010 would necessarily represent more information, but it doesn't! Throw two such strings in a bag, and your bag now contains less than 8 bits of ...

The Big Bounce

2016 was the Year of the "Big Bounce." Everyone has heard of the Big Bang, the idea that, about fourteen billion years ago, the universe emerged from nothingness through some sudden quantum event into an expanding space-time filled with hot matter and radiation. Many know that the Big Bang alone cannot explain the remarkably uniform distribution of matter and energy observed today or the absence of curves and warps that one might expect after a sudden quantum event. In order to account for these observations, an enhancement has been added, a brief epoch of superluminal expansion, known as inflation, that immediately follows the bang. Inflation added to the Big Bang was supposed to explain how the turbulent and twisted conditions following a bang could have been stretched out, leaving behind a smooth universe except for a pattern of tiny variations in temperature and energy. But neither the Big Bang nor inflation are proven ideas, and there are good reasons to consider an alternativ...

Cosmological Constant, or Vacuum Energy

A hundred years ago, in 1917, Albert Einstein had a problem. He had just come up with a beautiful new theory of gravity, called General Relativity. But the theory predicted that the universe should either expand or contract. Even for Einstein, this was a bridge too far. The universe, though it might have had a beginning, certainly did not appear to be changing. General Relativity is a very rigid theory: little can be changed about it without entirely destroying its elegant mathematical structure. The only wiggle room was a single quantity which Einstein called the "cosmological constant." If he assumed that this quantity was zero, the equations looked particularly simple. But then they also required the universe to be dynamical. The gravity of ordinary matter (such as galaxies) is attractive. Introducing a positive cosmological constant adds a repulsive counterforce. By setting the cosmological constant to a particular, nonzero value, at which the two tendencies precisely cancel each o...

Adaptive Preference

Adaptive preference is a concept that illuminates what happens both in the lab and in life. An adaptive preference results when we bend aspiration towards expectation in light of experience. We come to want what we think is within our grasp. More than a simple "reality check," adaptive preference formation involves disciplining one's motivational structure with the benefit of hindsight. Much of what passes for "wisdom" in life is about the formation of adaptive preferences. When the social psychologist Leon Festinger suggested the idea in the 1950s, it provided a neat account of how people maintain a sense of autonomy while under attack by events beyond their control. He might have been talking about how the US and the USSR held their nerve in Cold War vicissitudes, but in fact he was talking about how a millennial religious cult continued to flourish even after its key doomsday prediction had failed to materialize. In the 1980s, the social and political philosopher Jon Elster brillian...

Antagonistic Pleiotropy

Aging comes from evolution. It isn't a bug or a feature of life; it's an inevitable side effect. Exactly why evolution favors aging is controversial, but plainly it does; all creatures die. It's not a curse from God or imposed by limited natural resources. Aging arises from favoring short-term benefits, mostly early reproduction, over long-term survival, when reproduction has stopped. Thermodynamics doesn't demand senescence, though early thinkers imagined it did. Similarly, generic damage or "wear and tear" theories can't explain why biologically similar organisms show dramatically different lifespans. Most organisms maintain themselves efficiently until adulthood and then, after they can't reproduce anymore, succumb to age-related damage. Some die swiftly, like flies, and others like we humans can live far beyond reproduction. Peter Medawar introduced the idea that ageing was a matter of communication failure between generations. Older organisms have no way to pass on genes that help...

Multiverse

An astonishing concept has entered mainstream cosmological thought: it deserves to be more widely known. Physical reality could be hugely more extensive than the patch of space and time traditionally called "the universe." Our cosmic environment could be richly textured, but on scales so vast that our astronomical purview is restricted to a tiny fraction: we're not aware of the "grand design," any more than a plancton whose "universe" was a spoonful of water would be aware of the world's topography and biosphere. We may inhabit a "multiverse." However powerful our telescopes are, our vision is bounded by a horizon: a shell around us, delineating the distance light can have travelled since the big bang. But this shell has no more physical significance than the circle that delineates your horizon if you're in the middle of the ocean. There are billions of galaxies within our horizon. But we expect far more galaxies lying beyond. We can't tell just how many. If space stretched far enough,...

Anthropomorphism

Anthropomorphism is the attribution of human characteristics, qualities, motivations, thoughts, emotions, and intentions to non-human beings and even non-living objects. Writers and poets have freely used anthropomorphism in fictional and non-fictional narratives and, although this attribution has been a powerful and effective artistic device, in science it has been largely abandoned. The successes of the reductionist approach in physics and chemistry motivated similar methodologies in biology and psychology. Anthropomorphism was considered an error in the context of scientific reductionism. However, it has remained curiously effective in certain areas of biology and psychology despite being controversial. For example, the very inspiration for this year's Edge Question, Richard Dawkins introduction of the selfish gene meme, was a brilliant use of anthropomorphism (selfishness) to introduce a crucial concept in evolutionary theory. Thus the view that the tendency to anthropomorphiz...

Commitment Devices

Arguments over which species makes for the best pet are deeply unproductive: Clearly, those with different views are deeply misguided. Turtles, say, are easy: they sit around, chewing slowly. Dogs, say, are difficult: they run around, chewing rapidly. But there is a hidden benefit to some choices, unbeknownst to their owners. It's the fact that turtles are passive and dogs active that's the key. The Dog, it turns out, needs to go for walks—and so dog owners get a little bit of exercise every day. And, what is the dog's absolute favorite activity in the world? Meeting (and sniffing) other dogs, who happen to be attached to humans via their leashes—and so dog owners get a little of socializing every day as well. Research shows that getting a little exercise and chatting with strangers contributes to our well-being. Now, we could just decide: I'm going to go for a walk and chat with new people today. And repeat that to ourselves as we press play on another episode of Breaking Bad. But bec...

Mismatch Conditions

Assuming that you fear getting sick and dying, you really ought to think more about Mismatch Conditions. They are also a fundamental evolutionary process. Mismatch conditions are problems, including illnesses, that are caused by organisms being imperfectly or inadequately adapted to novel environmental conditions. As extreme examples, a chimpanzee adapted to the rainforests of Africa would be hopelessly mismatched in Siberia or the Sahara, and a hyena would be mismatched to a diet of grass or shrubs. Such radical mismatches almost always cause death and sometimes cause extinction. Mismatches, however, are typically more subtle and most commonly occur when climate change, dispersal or migration alters a species' environment, including its diet, predators, and more. Natural selection occurs when heritable variations to these sorts of mismatches affect offspring survival and reproduction. For instance, when tropically adapted humans who evolved in Africa dispersed to temperate habitats s...

Networks

Biological, human, and organizational realities are networked. Complex environments are networks. Computers are networked. Epidemics are networks. Business relations are networked. Thought and reasoning are in neural networks. Emotions are networked. Families are networks. Politics are networked. Culture and social relations are, too. Your network is your net worth. Yet the general public does not yet "speak networks." Network concepts are still new to many, and not widely enough spread. I have in mind structural traits like peer-to-peer and packet switching, process qualities such as assortativity, directionality and reciprocity, indicators such as in- and out-degree, density, centrality, betweenness, multiplexity and reciprocity, and ideas such as bridging vs. bonding, Simmelian cliques, network effects and strength of ties. These amount to a language and analytical approach whose time has come. Much of scientific thought in the last century, especially in the social and life science...

Mysterianism

By leaps, steps, and stumbles, science progresses. Its seemingly inexorable advance promotes a sense that everything can be known and will be known. Through observation and experiment, and lots of hard thinking, we will come to explain even the murkiest and most complicated of nature's secrets: consciousness, dark matter, time, the full story of the universe. But what if our faith in nature's knowability is just an illusion, a trick of the overconfident human mind? That's the working assumption behind a school of thought known as mysterianism. Situated at the fruitful if sometimes fraught intersection of scientific and philosophic inquiry, the mysterianist view has been promulgated, in different ways, by many respected thinkers, from the philosopher Colin McGinn to the cognitive scientist Steven Pinker. The mysterians propose that human intellect has boundaries and that some of nature's mysteries may forever lie beyond our comprehension. Mysterianism is most closely associated with the...

Somatic Evolution

Cancer seems inscrutable. It has been variously described as a disease of the genome, a result of viral infection, a product of misbehaving cells, a change in metabolism, and cell signaling gone wrong. Like the eight blind people touching different parts of an elephant, these all indeed describe different aspects of cancer. But the elephant in the room is that cancer is evolution. Cancer is a form of evolution within our body, the "soma"—cancer is somatic evolution. Take that spot on your arm as proof that some of your cells are different from others: some darker, some lighter. This difference is also heritable when one of your body's cells divides into two daughter cells, encoded as a mutation in the cell's DNA, perhaps caused by sun exposure. Much of somatic evolution is inconsequential. But some of the heritable variation within a human body may be of a kind that makes a more substantial change than color: it produces cells that divide faster, setting in motion a chain of events ...

Maxwell's Demon

Carl Sagan spoke too soon when he spoke about demons. Modern science, he told his numerous followers, banished witches, demons and other such creatures from this world. Simply spread flour on the floor and check for suspicious footprints—this kind of reasoning, he claimed in The Demon-Haunted World, characterizes sound, scientific thinking. So why is Maxwell's demon still on the frontlines of science? Since he was first conjured in 1874, modern day inquisitors have valiantly chased after him with math and physics instead of holy water. But rather than going the way of the phlogiston and the ether, he has emerged unscathed and is now a fixture in standard physics textbooks. Lest you think he is real, let me tell you he is not. But a demon he is in spades. He sorts, and sorting is at the origin of sorcery. Neat-fingered and vigilant, he can reverse time, momentarily violate the second law of thermodynamics, power a perpetual motion machine, and generate pockets of hellish heat in substan...

Zone of Proximal Development

Clear instruction is essential for learning. But even the clearest instruction can be of limited use, if the learner is not at the right place to receive it. Psychologist Lev Vygotsky had a remarkable insight about how we learn. He coined the term zone of proximal development to describe a sweet spot for learning in the gap between what a learner could do alone, and what that learner could do with help from someone providing knowledge or training just beyond the learner's current level. With such guidance, learners can succeed on tasks that were too difficult for them to master on their own. Crucially, guidance can then be taken away, like scaffolding, and learners can succeed at the task on their own. The zone of proximal development introduces three interesting twists to cognitive scientists' notions of learning. First, it might lead us to reconsider notions of what a person "knows" and "knows how to do." Instead, conceptualizing peak knowledge or abilities as a learner's current max...

Confusion

Commonly, confusion denotes bewildering uncertainty, often associated with delirium or even dementia. From the confusion of languages in the Genesis of the bible, to Genesis the band, broader audiences mostly encounter negative aspects of confusion. This short text aims to shed a different light on the concept: Confusion that can be both positive and negative, sometimes both at the same time; Confusion as a subject of scientific interest; Confusion as a phenomenon that can't be ignored, that requires scientific understanding, and that needs to be designed and moderated. A convenient tool to measure confusion in a system is the so-called confusion matrix. It is used in linguistics and computer science, in particular machine learning. In principle, the confusion matrix is a table, where all criteria in the dimension of rows are compared to all criteria in the dimension of columns. A simple example is to compare all letters of the alphabet spoken by an English native, with the letters act...

Emotion Contagion

Emotions are contagious. They are rapidly, frequently, and even at times automatically transmitted from one person to the next. Whether it be mind-boggling awe watching the supermoon display its lunar prowess or pangs of anger observing palpable racial injustice, one feature remains salient: we can and often do "catch" the emotions of others. The notion that emotions are contagious dates back as early as 1750s when Adam Smith documented the seamless way people tend to mimic the emotional expressions, postures, and even vocalizations of the people we interact with. In the late 1800s, Charles Darwin further emphasized that this highly contagious nature of emotions was fundamental to the survival of humans and nonhumans alike in transmitting vital information among group members. These prescient observations underscore the fact that emotion contagion is pervasive and universal and, hence, why it ought to be more widely known. More recent scientific models of emotion contagion expound the...

Empathic Concern

Empathy has gotten a bad reputation of late, largely undeserved. That negative spin occurs because people fail to understand the nuanced differences between three aspects of empathy. The first kind, cognitive empathy, allows me to see the world through your eyes: to take your perspective and understand the mental models that make up your lens on events. The second kind, emotional empathy, means I feel what your feel; this empathy gives us an instant felt sense of the other person's emotions. It's the third kind, empathic concern, that leads us to care about the other person's welfare, to want to help them if they are in need. Empathic concern forms a basis for compassion. The first two, while essential for intimate connection, can also become tools in the service of pure self-interest. Marketing and political campaigns that manipulate people's fears and hatreds require effective cognitive and emotional empathy—as do conmen. And, perhaps, artful seductions. It's empathic concern—car...

Effect Modification

Enshrined in the way much medical research is done is the tacit assumption that an exposure has an effect on an outcome. To quote Wikipedia: "Effect modification occurs when the magnitude of the effect of the first exposure on the outcome—the association—differs depending on the level of a third variable. In this situation, computing the overall effect of the association is misleading." The reach of Effect Modification (EM) is wildly underappreciated. Implications challenge the core of how medicine—and indeed science—are practiced. The results of randomized, double-blinded, placebo-controlled trials (RCTs) are the foundation on which modern medicine rests. RCTs are exalted as the gold standard of study designs. These define treatment approaches, which are propelled into use through "clinical practice guidelines," with teeth in their implementation imposed through "performance pay" to doctors. But, there is a problem. Often, a single estimate of effect is generated for a given outco...

Gravitational Lensing

Every day you play with the light of the universe. Subtle visitor, you arrive in the flower and the water... These lines from one of Pablo Neruda's poems captures the essence of light bending—gravitational lensing—that is ubiquitous in the cosmos. Re-conceptualizing gravity in his theory of general relativity, Einstein postulated the existence of space-time, a four-dimensional sheet to describe the universe. This is a beautiful marriage between geometry and physics, wherein all matter, both ordinary and exotic, in the universe would cause potholes in the fabric of space-time. So that matter would dictate how space-time curved, and space-time in-turn would determine how matter moves. One important consequence of this formulation is the impact that the rumpled fabric of space-time would have on the propagation of light in the universe. Light emitted by distant galaxies will get deflected by the potholes generated by all the mass en-route that it encounters. This phenomenon of the bending...

Fallibilism

Fallibilism is the idea that we can never be 100% certain that we are right, and must therefore always be open to the possibility that we are wrong. This might seem a pessimistic notion, but it is not. Ironically, this apparent weakness is a strength; for admitting one's mistakes is the first step to learning from them, and overcoming them, in science and society. Fallibilism lies at the heart of the scientific enterprise. Even science's most well-established findings—the "laws" of nature—are but hypotheses that have withstood scrutiny and testing thus far. The possibility that they may be wrong, or be superseded, is what spurs the generation of new alternative hypotheses, and the search for further evidence that enables us to choose between them. This is what scientific progress is made of. Science rightly champions winning ideas, ideas that have been tested and have passed, and dispenses with those that have been tested and have failed, or are too vague to be tested at all. Fallibili...

Metamaterials

First demonstrated in 1999 by a group of researchers led by physicist David R. Smith, metamaterials are now on the cusp of transforming entire industries. The term generally refers to synthetic composite materials that exhibit properties not found in nature. What Smith demonstrated was the ability to bend light waves in directions—described as "left-handed"—not observed in natural materials. As a field of engineering metamaterials are perhaps the clearest evidence that we are in the midst of a materials revolution that goes far beyond the impact of computing and communications. The concept has been speculated about for more than a century, particularly in the work of Russian physicist Victor Veselago during the 1960s. However, the results of Smith's group touched off a new wave of excitement and experimentation in the scientific community. The notion captured the popular imagination briefly some years ago with the discussion of the possibility of invisibility cloaks, however, today...

Future Self-Continuity

Five years from now, what will your future self think of your current self? Will you even be the same person? Over a century before the birth of Christ, Bactrian King Milinda challenged the Buddhist sage Nagasena to define identity. The Buddhist responded by inquiring about the identity of the king's chariot: "...is it the axle? Or the wheels, or the chassis, or reins, or yoke that is in the chariot? Is it all of these combined, or is it apart from them?" The king was forced to concede that his chariot's identity could not be reduced to its' pieces. Later, Greek scholar Plutarch noted that the passage of time further complicates definitions of identity. For example, if a ship is restored piece by piece over time, does it retain its' original identity? As with Theseus' reconstructed ship, the paradox of identity applies to our constantly regenerating bodies (and their resident brains). Flipping in time from the past to the future, to what extent can we expect our identity to change over t...

Synaptic Transfer

For all its fiber-enabled, live-video-streaming, 24/7-connected promise, our information network encapsulates a fundamental flaw: it's proving a suboptimal system for keeping the world informed. While it embraces nodes dedicated to propagating a rich seam of information, because the internet's governing algorithms are optimized to connect us to what they believe we are already looking for, we tend to retreat into familiar and comfortably self-reinforcing silos: idea chambers whose feeds, tweets and updates inevitably echo our pre-existing prejudices and limitations. The wider conversation, a precondition for a healthy intellectual culture, isn't getting through. The signals are being blocked. The algorithmic filter is building ever-higher walls. Facts are being invalidated by something called "post-truth." And that's just not healthy for the quality of informed public debate that Edge has always celebrated. Thankfully a solution is suggested by neural networks of a biological kind. Ins...

Fixpoint

Given the operation of squaring a number, there are two numbers that are special, because the operation doesn't change them: 0 and 1. 0 squared is 0, and 1 squared is 1, but square any other number and the output will differ from the input. These special numbers are called fixpoints (of squaring). In general, a fixpoint is a value (or state of a system) that is left unchanged by a particular operation. This concept, easily definable by the brief equation x=f(x), is at the essence of several other ideas with great practical significance, from Nash equilibria (used in economics and social sciences, to model failures of cooperation) to stability (used in control theory, to model systems ranging from aircraft to chemical plants) to PageRank (the foremost web search algorithm). It even appears in work at the foundations of logic, to give definition to truth itself! A prevalent example in everyday life is the occurrence of fixpoints in any strategic context ("game") with multiple players. Su...

Sexual Selection

Having been born in the tiny Welsh village of Llanbadoc 141 years after Alfred Russel Wallace, I have always had a sneaking sympathy with people eager to give Wallace joint billing with Darwin for "The Best Idea Anyone Ever Had." Having said which, I don't think Evolution by Natural Selection was Darwin's best or most valuable idea. Earlier thinkers, from Lucretius to Patrick Matthew, had grasped that there was something inevitably true in the idea of Natural Selection. Had neither Darwin or Wallace existed, someone else would have come up with a similar theory; many practical people, whether pigeon fanciers or dog breeders, had already grasped the practical principles quite well. But, for its time, sexual selection was a truly extraordinary, out-of-the-box idea. It still is. Once you understand sexual selection—along with costly signaling, Fisherian runaway, proxies, heuristics, satisficing and so forth—a whole host of behaviors which were previously baffling or seemingly irration...

Satisficing

Herbert Simon contributed importantly to our understanding of a number of problems in a wide array of disciplines, one which is the notion of achievement. Achievement depends not only on ability and the problem at hand (including information available and the environment), but also one's motivation and targets. Two of Simon's many insights were how much effort it takes to become an "expert" at an endeavor requiring a special skill (using chess as a model, the answer is—very approximately—10,000 hours), and how objectives are accomplished: whether individuals maximize, optimize, or rather accept or even seek an apparently lesser outcome, that is, satisfice. Satisficing recognizes constraints on time, capacity and information, and the risk and consequences of failure. In Simon's own words from his 1956 paper on the subject: "...the organism, like those of the real world, has neither the senses nor the wits to discover an 'optimal' path—even assuming the concept of optimal to be clearly d...

Length-Biased Sampling

Here are three puzzles. And here is a twist: these are all the same puzzle. The solution is adopting the right perspective. Consider the family puzzle. One side is about what parents do; the other side is about what kids experience. If families all had the same number of kids, these perspectives would coincide: The context parents create is the context kids live in. But when families aren't all the same size, it matters whose perspective you take. Imagine trying to figure out the average family size in a particular neighborhood. You could ask the parents how many kids they have. Big families and small families will count equally. Or you could ask the children how many siblings they have. A family with five kids will show up in the data five times, and childless families won't show up at all. The question is the same: How big is your family? But when you ask kids instead of parents, the answers are weighted by the size of the family. This isn't a data error so much as a trick of reality...

Construal

Here is a trivial fact about our mental lives. So trivial, it is rarely even noticed. And it is hard to talk about without sounding sophisticated. The post-modernists have explored versions of it, but the notion I mean to promote—the notion of "construal"—is painfully obvious. It refers to the fact that our attitudes and opinions and choices pertain to things not as they are in the world, but as they are represented in our minds. Economic theorizing presumes that people choose between options in the world: Job A versus Job B, or Car A versus Car B. From the point of view of a psychologist, however, that presumption is really quite radical: When a person is presented with a choice between options A and B, she chooses not between A and B as they are in the world, but rather as they are represented by the 3-pound machine she carries behind the eyes and between the ears. And that representation is not a complete and neutral summary, but rather a selective and constructed rendering—a constr...

Bounded Optimality

How are we supposed to act? To reason, to make decisions, to learn? The classic answer to this question, hammered out over hundreds of years and burnished to a fine luster in the middle of the last century, is simple: update your beliefs in accordance with probability theory and choose the action that maximizes your expected utility. There's only one problem with this answer: it doesn't work. There are two ways in which it doesn't work. First, it doesn't describe how people actually act. People systematically deviate from the prescriptions of probability and expected utility. Those deviations are often taken as evidence of irrationality—of our human foibles getting in the way of our aspirations to intelligent action. However, human beings remain the best examples we have of systems that are capable of anything like intelligent action in many domains. Another interpretation of these deviations is thus that we are comparing people to the wrong standard. The second way in which the classi...

Allostasis

How to respond to change? Try to keep your inner state constant or instead adjust your inner state according to the external change? Staying constant inside is the classic idea of homeostasis, pioneered by the physiologist Claude Bernard in 1865 with the name coined by physiologist Walter Cannon in 1926. Homeostasis describes the essential feature of all living things that they define an inside and keep it stable in an unstable environment. Body temperature is a classic example. Homeostasis is, however, not very dynamic or darwinian: the business of living creatures is not to optimize their interior state. It is to survive. Whether or not the internal state is stable. Therefore, the concept of allostasis was created in the 1980ies by neuroscientist Peter Sterling and coworkers. The word allostasis means a changing state, where homeostasis means staying in about the same state. The idea of allostasis is that the organism will change its inner milieu to meet the c...

Phenotypic Plasticity

Humans all over the world share the same genome, the same neural architecture and the same behavioral niche (three-generational system of resource provisioning, long-term pair-bonding between men and women, high levels of cooperation between kin and non-kin). At the same time, human cultures are highly variable. Some societies see revenge as a duty, others as a sin; some regard sex as a pleasure, others as a danger, and some reward innovations while others prefer traditions. In many instances, these cultural differences are robust, and can last for millennia despite cultural contacts, political assimilation or linguistic replacement. How can we account for such variability? Traditionally, it is assumed that cultural variability cannot be explained by species-specific evolved mechanisms and that it must be the product of socially transmitted norms in the forms of religious beliefs, informal enforcement or political conquest. This assumption is based on a common misconception about natur...

Supernormal Stimuli

Humans and other animals fall for hyperbole. Exaggeration is persuasive, subtly exists in it shadows. In a famous set of studies done in the 1950's biologist and ornithologist Niko Tinbergen created "supernormal stimuli," simulacra of beaks and eggs and other biologically salient objects, that were painted, primped and blown up in size. In these studies herring gull chicks pecked more at big red knitting needles than at adult herring gull beaks, presumably because they were redder and longer than the actual beaks. Plovers responded more to eggs with striking visual contrast (black spots on white surround) than to natural but drabber eggs with dark brown spots on light brown surround. Oystercatchers were willing to roll huge eggs into their nests to incubate. Later studies, as well as recording in the wild show supernormal stimuli hijacking a range of biologically driven responses. For example, female stickleback fish get swollen bellies when they are ripe with eggs. When Tinbergen's st...

On Average

Humans have fewer than two legs... ...on average. It takes a moment to realize the logic of that sentence... Just a single "one-legged pirate" moves down the average for all of mankind, to just a fraction under two. Simple and true—but also counter-intuitive. A variation moving the average upwards instead: Billionaire walks into a bar. And everyone is a millionaire... ...on average. That's all rather basic statistics, but as obvious as it might seem, amongst the abundance of highly complex concepts and terms in this essay collection, many scientific truths are not easily grasped in everyday life and the basic tools of understanding are woefully underutilized by the general public. They are badly taught—if indeed they are part of the curriculum at all. Everyone today is totally surrounded by practical math. Leaving high school it should be standard issue knowledge to understand how credit cards work, compounding interest, or mortgage rates. Or percentage discounts, goods on sale a...

"On The Average"

I'm voting for this concept, one that is so central to the scientific process, so much a given, that hardly any scientist ever actually speaks those words. Scientists present their work—say, "We manipulated Variable X, and observed that this caused Z to happen," or "We measured this and found that it takes Z amount of time to happen." And when they do, most of the time what they're actually saying is, "We manipulated Variable X, and observed that, on the average, this caused Z to happen." "We measured this and found that, on the average, it takes Z amount of time to happen." Everyone knows this. Of course. Everyone in a population doesn't have the exact same levels of something or other in their bloodstream. A causes B to happen most of the time, but not every single time. There's variability. When scientists present their data, they typically display the average—the mean, the X on a graph, the bar of a particular height in the figure. And it always comes with an "error term—a measure ...

The Symbol Grounding Problem

I.J. Good, a collaborator of Alan Turing's during World War II, once wrote that a machine more intelligent than humans would be the "last invention" we make. Many believe that our society is about to reach this point, as smart machines increasingly invade our daily lives and imaginations. This invasion is proceeding along two fronts. Such machines are increasingly to blame for economic change, leading some people to question the necessity of work altogether. But, more deeply, we wonder whether such ultraintelligent machines will be "like us": they may think, but will they feel? To help anchor these latter kinds of questions, Stevan Harnad formulated the symbol grounding problem. For a machine, it's problematic to learn what the symbols that make up human languages mean by simply transforming heard words into spoken words. It's like trying to learn Egyptian hieroglyphs using a dictionary in which each hieroglyph is defined using other hieroglyphs. Consider this exchange I just had with ...

Intertemporal Choice

If I offered to give you $20 today or $100 in a year, which would you choose? It's a pretty straightforward question, and, truth be told, one that has a logical answer. Unless you need that $20 to ensure your near-term survival, why not wait for the bigger prize if it were sure to come. After all, when was the last time that any reputable financial institution offered an investment vehicle guaranteed to quintuple your money in 365 days? Yet, if you pose this question to the average person, you'll be surprised to find that most will opt to take the $20 and run. Why? To understand that, and the implications it holds for decisions in many domains of life, we first have to put the framework of the decision in context. This type of decision—one where the consequences of choices change over time—is known as an "intertemporal choice." It's a type of dilemma well-studied by economists and psychologists, who often facepalm at the seemingly irrational decisions people make when it comes to inves...

The Illusion of Explanatory Depth

If you asked one hundred people on the street if they understand how a refrigerator works, most would respond, yes, they do. But ask them to then produce a detailed, step-by-step explanation of how exactly a refrigerator works and you would likely hear silence or stammering. This powerful but inaccurate feeling of knowing is what Leonid Rozenblit and Frank Keil in 2002 termed, the illusion of explanatory depth (IOED), stating, "Most people feel they understand the world with far greater detail, coherence, and depth than they really do." Rozenblit and Keil initially demonstrated the IOED through multi-phase studies. In a first phase, they asked participants to rate how well they understood artifacts such as a sewing machine, crossbow, or cell phone. In a second phase, they asked participants to write a detailed explanation of how each artifact works, and afterwards asked them re-rate how well they understand each one. Study after study showed that ratings of self-knowledge dropped drama...

Sleeper Sensitive Periods

If you moved from the United States to France as a child you would likely become fluent in French in a short period of time, but if you moved to France as an adult you might never become fluent. This difference in the capacity to learn language exists because there are sensitive periods in development when the brain is particularly plastic and able receive and retain information with greater efficacy. There is a well-established field of sensitive period biology that seeks to explain how people learn to speak, how birds learn to sing, and how our sensory systems wire up among other things. The field has been particularly successful in explaining how the brain coordinates the information streaming in from the two eyes to allow binocular vision useful for depth perception. In the last century, it was discovered that when a person was born with a "lazy" eye or had their vision clouded in one eye by a cataract then their binocular vision would be impaired for a lifetime. However, if a corr...

Double Blind

In 1620 Sir Francis Bacon published Novum Organum and kicked off the scientific revolution by defining its basic method: hypothesis, experiment, and result. By 1687 we had Newton's Principia, and the rest is history. Today, public primary schools teach the Scientific Method. It's well known. It turns out that following the method is not so simple. People, including scientists, are not perfectly rational. People have biases and even when we try to be good, sometimes, unconsciously, we do wrong. When the outcome of an experiment has career implications, things start to get complicated. And when the outcome has financial implications for a powerful institution, people have been known to actively game the system. For example, starting in 1953 the Tobacco Industry Research Committee waged a war on truth, until it was dissolved as part of the master settlement in 1998. The stakes are high. Tobacco killed 100 million people in the 20th century. Climate change threatens our very way of life. I...

Habituation

In 1964 Robert Fantz published a brief paper in Science that revolutionized the study of cognitive development. Building on the idea that infants' gaze can tell you something about their processing of visual stimuli, he demonstrated that babies respond differently to familiarity and novelty. When infants see the same thing again and again, they look for less and less time—they habituate. When infants next see a new stimulus, they regain their visual interest and look longer. Habituation establishes the status quo—the reality you no longer notice or attend to. Subsequent generations of developmental psychologists have expanded on this methodological insight to probe the building blocks of human thinking. Capitalizing on the idea that babies get bored of the familiar and start to look to the novel, researchers can test how infants categorize many aspects of the world as same or different. From this, scientists have been able to investigate humans' early perceptual and conceptual discrim...

Coarse-Graining

In physics a fine-grained description of a system is a detailed description of its microscopic behavior. A coarse-grained description is one in which some of this fine detail has been smoothed over. Coarse-graining is at the core of the second law of thermodynamics, which states that the entropy of the universe is increasing. As entropy, or randomness, increases there is a loss of structure. This simply means that some of the information we originally had about the system has become no longer useful for making predictions about the behavior of a system as a whole. To make this more concrete, think about temperature. Temperature is the average speed of particles in a system. Temperature is a coarse-grained representation of all of the particles' behavior-the particles in aggregate. When we know the temperature we can use it to predict the system's future state better than we could if we actually measured the speed of individual particles. This is why coarse-graining is so important-it...

Epsilon

In statistical modeling the use of the Greek letter "epsilon" explicitly recognizes that uncertainty is intrinsic to our world. The statistical paradigm envisions two components: data or measurements drawn from the world we observe; and the underlying processes that generated these observed data. Epsilon appears in mathematical descriptions of these underlying processes and represents the inherent randomness with which the data we observe are generated. Through the collection and modeling of data we hope to make better guesses at the mathematical form of these underlying processes, with the idea that a better understanding of the data generating mechanism will allow us to do a better job modeling and predicting the world around us. That use of epsilon is a direct recognition of the inability of data driven research to perfectly predict the future, no matter the computing or data collection resources. It codifies that uncertainty exists in the world itself. We may be able to understand ...

Algorithms

In the 20th century, we gained a deep understanding of the physical world using equations and the mathematics of continuous variables as the chief source of insights. A continuous variable varies smoothly across space and time. Unlike the simplicity of rockets, which follow Newton's laws of motion, there isn't a simple way to describe a tree. In the 21st century, we are making progress understanding the nature of complexity in computer science and biology based on the mathematics of algorithms, which often have discrete rather continuous variables. An algorithm is a step-by-step recipe that you follow to achieve a goal, not unlike baking a cake. Self-similar fractals grow out of simple recursive algorithms that create patterns resembling bushes and trees. The construction of a real tree is also an algorithm, driven by a sequence of decisions that turn genes on and off as cells divide. The construction of brains, perhaps the most demanding construction project in the universe, is also ...

Phylogeny

In what ways are you related to the contents of your salad? Or to the ingredients of a slice of pepperoni pizza? Or whatever your next meal might be? Of course, consumption is an ecological relationship. Your body digests and absorbs the nutrients from your food, which provide energy for your metabolism and material components for your cells. But another fundamental kind of relationship is more cryptic, and in many ways more profound. The answer comes from one of Charles Darwin's least appreciated revolutionary ideas. Darwin is, of course, duly famous for his discovery of the process of natural selection, which is among the most successful concepts in the history of science. Darwin also discovered the process of sexual selection, which he viewed as an independent mechanism of evolution. But Darwin was the first person ever to imply that all of life came from a single or a few common origins, and had diversified over time through speciation and extinction to become the richness of the...

Included Middle

Included Middle is an idea proposed by Stéphane Lupasco (in /The Principle of Antagonism and the Logic of Energy/ in 1951), further developed by Joseph E. Brenner and Basarab Nicolescu, and also supported by Werner Heisenberg. The notion pertains to physics and quantum mechanics, and may have wider application in other domains such as information theory and computing, epistemology, and theories of consciousness. The Included Middle is a theory proposing that logic has a three-part structure. The three parts are the positions of asserting something, the negation of this assertion, and a third position that is neither or both. Lupasco labeled these states A, not-A, and T. The Included Middle stands in opposition to classical logic stemming from Aristotle. In classical logic, the Principle of Non-contradiction specifically proposes an Excluded Middle, that no middle position exists, /tertium non datur/ (there is no third option). In traditional logic, for any proposition, either that prop...

Emptiness

It is said in the Doctrine of the Mean, written by the grandson of Confucius, that the greatest knowledge, including both scientific concepts and human realizations, comes only from the everyday lives with an empty mind. The title of the book, Doctrine of the Mean, does not mean the middle way of the two extremes but the emptiness of the mind in everyday life. We call it as Moderation. This teaching of the Doctrine of the Mean connects its essence to Zarathustra by Nietzsche, as Heidegger explains in his book, What is Thinking. They all stressed that we cannot think without emptying our minds in the everyday lives. If one can think, one can do everything: Confucius' grandson called it a scholar or scientist, while Nietzsche called it Zarathustra. After crossing the river with a raft, we have to abandon the raft to climb the mountain. Existing knowledge helps but guides us too much that it hinders us from obtaining newly formed representations to become the new corresponding concepts. W...

The Scientist

It is said that Charles Darwin left on the Beagle as a Natural Philosopher and returned as a Scientist. Not because of anything he did while on the voyage, although he did plenty, but because in 1833 Cambridge professor and Master of Trinity College, the polymath William Whewell (pronounced "hewell") invented the word scientist. It was not the only word he coined (he also came up with ion, cathode and anode for Michael Faraday), but it is perhaps the most influential. Until Whewell invented the word all those people we would today call scientists—beginning with Aristotle and including Newton, Galileo, Mendel, Galen—were known as Natural Philosophers. The distinction is revealing. Among the purposes of Natural Philosophers was to understand the mind of the creator through the study of the natural world. The study of science was an intellectual pursuit not distinct from theological examination. But that was changing. Whewell's suggestion of the term scientist was in response to a challen...

Systemic Bias

It is said, by those who believe in the devil, that his greatest achievement was convincing the rest of the world that he did not exist. There are two biases that play a similar role in our search for objective knowledge and our goal of making better decisions. These are optimism bias and skepticism bias. Their true threat come from the fact that many people are unaware of their existence. And yet once recognized, you'll see these biases everywhere. Optimism is not only infectious but effective. Enthusiasm is often a requirement for success. During World War II, the U.S. Army Corps of Engineers adopted as a motto an aphorism from a French novelist: "The difficult we do quickly. The impossible takes a little longer." Consider optimism and skepticism bias in the field of energy. Some say solar power is too expensive or too intermittent? Rather than address these directly, we can substitute optimism: let's let loose American can-do and solve those challenges! (In the world today there l...

Counting

John McCarthy, the late co-founder of the field of artificial intelligence, wrote, "He who refuses to do arithmetic is doomed to talk nonsense." It seemed incongruous that a professor who worked with esoteric high level math would be touting simple arithmetic, but he was right; in fact in many cases all we need to avoid nonsense is the simplest form of arithmetic: counting. In 2008, the US government approved a $700 billion bank bailout package. A search for the phrase "$700 million bailout" reveals hundreds of writers who were eager to debate whether this was a prudent or rash, but who couldn't distinguish the difference between $2 per citizen and $2,000 per citizen. Knowing the difference is crucial to understanding the efficacy of the deal, and is just a matter of counting. Consider the case of a patient who undergoes a routine medical screening and tests positive for a disease that affects 1% of the population. The screening test is known to be 90% accurate. What is the chance th...

Variety

Leibniz was famously satirized by Voltaire, in his play Candide, as saying that ours is the best of all possible worlds. While that played well on the stage, what Leibniz actually wrote, in 1714, in his Monodology, was a good deal more interesting. He did argue that God chose the one real world from an infinitude of possible worlds, by requiring it to have "as much perfection as possible." But what is often missed is how he characterized degrees of perfection. Leibniz defined a world with "as much perfection as possible" to be one having "as much variety as possible, but with the greatest order possible." I believe that Leibniz's insight of a world that optimizes variety, subject to "the greatest order possible", is a powerful concept that could be helpful for current work in biology, computer science, neuroscience, physics and numerous other domains including social and political theory and urban planning. To explain why, I have to define variety. I believe we ought to see variety as ...

Homeostasis

Life, as we know it, requires some degree of stability—both internally and externally. Consider a bacterium like E. coli that needs to maintain its internal copper concentrations within a narrow range: too much copper would kill the cell, while too little would impede important metabolic functions that rely on copper atoms as catalytic centers of enzymes. Keeping copper concentrations within the required range—copper homeostasis—is achieved through a negative feedback loop: the bacterium possesses internal sensors that react to sub-optimal copper levels by changing the production rate of proteins that pump copper out of the cell. This feedback system has its limits, though, and most bacteria succumb to too much copper in their environment—storing water in copper containers is an age-old strategy to keep it fresh. Human cells not only need elaborate systems to achieve internal homeostasis of many types of molecules. In addition, they also require a precisely tuned environment. Our cel...

Maladaptation

Many years ago, Francis Crick promoted (attributing it to his long-time collaborator Leslie Orgel) an aphorism that dominates the thinking of most biologists: "Evolution is cleverer than you are." This is often viewed as a more succinct version of Theodosius Dobzhansky's famous dictum: "Nothing in biology makes sense except in the context of evolution." But these two observations, at least in the terms in which they are usually interpreted, are not so synonymous as they first appear. Most of the difference between them comes down to the concept of maladaptation. A maladaptive trait is one that persists in a population in spite of inflicting a negative influence on the ability of individuals to pass on their genes. Orgel's rule, extrapolated to its logical conclusion that evolution is pretty much infinitely clever, would seem to imply that this can never occur: evolution will always find a way to maximize the evolutionary fitness of a population. It may take time to respond to changed c...

Surreal Numbers

Merriam-Webster's 2016 word of the year is surreal: "It's a relatively new word in English, and derives from surrealism, the artistic movement of the early 1900s that attempted to depict the unconscious mind in dreamlike ways as 'above' or 'beyond' reality. Surreal itself dates to the 1930s, and was first defined in a Merriam-Webster dictionary in 1967. Surreal is often looked up spontaneously in moments of both tragedy and surprise..." One of the lesser-known applications of the word belongs to the Princeton mathematician John Horton Conway who discovered surreal numbers circa 1969. To this day, he wishes more people knew about the surreals, in hopes that the right person might put them to greater use. Conway happened upon surreal numbers—an elegant generalization and vast expansion of the real numbers—while analysing games, primarily the game Go, a popular pastime at math departments. The numbers fell out of the games, so to speak, as a means of classifying the moves made by each playe...

Relative Deprivation

Middle class Americans don't live like kings—they live better than kings. If you showed Henry VIII the average American's living conditions, he would be awe-struck. While most Americans do not have giant castles or huge armies, we have luxuries that the royalty of yesteryear could scarcely dream about: big screen TVs and the Internet, fast cars and even faster planes, indoor plumbing and innerspring mattresses, and vastly improved medical care. Despite this incredible standard of living, most of us don't feel like kings. Instead, we feel like paupers because of relative deprivation. Relative deprivation is that idea that people feel disadvantaged when they lack the resources or opportunities of another person or social group. An American living in a trailer park has an objective high standard of living compared with the rest of the world and the long tail of human history: they have creature comforts, substantial freedom of choice, and significant safety. Nevertheless, they feel de...

Time Window

Modern biology is guided by a principle that has been summarized by Theodosius Dobzhansky in 1973 with the memorable sentence: "Nothing in biology makes sense, except in the light of evolution." On the basis of this conceptual frame I both generalize, but also suggest more specifically that nothing in neurobiology, psychology, the social sciences (or cognitive science in general), makes sense except in the light of synchronization, i.e., to create common time for temporally and spatially distributed sources of information or events. Without synchronization neural information processing, cognitive control, emotional relations, or social interactions would be either impossible or severely disrupted; without synchronization we would be surrounded by informational chaos, desynchronized activities, unrelated events, or misunderstandings. Synchronization as a fundamental principle is implemented on different operating levels by temporal windows with different time constants, from the sub-sec...

Negative Evidence

Negative evidence is a concept that deserves greater currency in the intellectual trades and popular culture. Negative evidence helps prove that something did not occur. University registrars routinely use negative evidence when they run a transcript check to prove that someone never got a degree at their university. Negative evidence is the epistemic dual to positive evidence. It is just that evidence that tends to prove a negative. So it collides headfirst with the popular claim that you cannot prove a negative. A more sophisticated version of the same claim is that absence of evidence is not evidence of absence. Both claims are false in general. It may well be hard to prove a negative to a high degree. That does not diminish the probative value of doing so. It took the invasion and occupation of Iraq to prove that the country did not have weapons of mass destruction. The weapons may still turn up someday. But the probability of finding any has long since passed from unlikely to high...

Homophily

No, homophily has nothing to do with sexual orientation. In the 1950s a pair of sociologists, Paul Lazarsfeld and Robert Merton, coined the term homophily to refer to the pervasive tendency of humans to associate with others who are similar to themselves. Even if you do not know homophily by name, it is something you have experienced throughout your life. In whatever elementary school you went to, in any part of the world, girls tended to be friends with girls, and boys with boys. If you went to a high school that had people of more than one ethnicity, then you saw it there. Yes, you may have been friends with someone of another ethnicity, but such friendships are the exception rather than the rule. We see strong homophily by age, ethnicity, language, religion, profession, caste, and income level. Homophily is not only instinctual—just watch people mingle at any large social event in which they are all strangers—it also makes sense for many reasons. New parents learn from talking ...

Uncertainty

Nothing feels better than being certain, but science has taught us over the years that certainty is largely an illusion. In science, we don't "believe" in things, or claim to know the absolute truth. Something is either likely or unlikely, and we quantify how likely or unlikely. That is perhaps the greatest gift that science can give. That uncertainty is a gift may seem surprising, but it is precisely for this reason that the scientific concept of uncertainty needs to be better and more broadly understood. Quantitatively estimating uncertainties—the hallmark of good science—can have a dramatic effect on the conclusions one draws about the world, and it is the only way we can clearly counteract the natural human tendency to assume whatever happens to us is significant. The physicist Richard Feynman was reportedly fond of saying to people, "You won't believe what happened to me today!" and then he would add "Absolutely nothing!" We all have meaningless dreams night after night, but dream...

Cumulative Culture

Over the 7 million years since humans and chimpanzees shared a common ancestor, the inventory of human tools has gone from a handful of stone implements to a technological repertoire capable of replicating DNA, splitting atoms, and interplanetary travel. In the same evolutionary timespan, the chimpanzee toolkit has remained relatively rudimentary. It was "tool innovation"—constructing new tools or using old tools in new ways—that proved crucial in driving increasing technological complexity over the course of human history. How can we explain this wide divergence in technological complexity between such closely related primate species? One possibility is that humans are unique among primate species in our capacity to innovate. If so, we might expect that innovation would be early-developing like walking or language acquisition. And yet there is little evidence for precocious innovation in early childhood. Although young children are inquisitive and keen to explore the word around them,...

Historiometrics

Over the centuries, reflective individuals have speculated about the causes of differences among individuals (who is talented and why, what makes certain persons influential) and among societies (why have certain cultures thrived and others vanished; which societies are bellicose and why). In the 19th century, scholars began systematic study of such issues; work in this vein has continued and expanded. This line of study has been dubbed historiometrics or, alternatively, cliometrics. These terms, while literally and etymologically appropriate, are hardly transparent or snappy—among the reasons that historiometric scholars and approaches have yet to receive due credit. Among continental scholars, the Belgian statistician Adolphe Quetelet is often credited with opening up this line of work. But in the Anglo-American scholarly community, the British polymath Francis Galton is generally seen as the patron saint of historiometric studies. As a member of the distinguished Darwin family, Galt...

Attractors

Quickly cool a piece of super-heated, liquid glass and a strange thing happens. The glass becomes hard, but very brittle—so much so that it may abruptly and startlingly shatter without warning. This is because the bonds between the molecules are under strain, and the cool temperature and low velocity means they cannot escape, as if caught in a negative equity trap with the neighbors from hell. And, like warring neighbors, eventually something gives way and the strain relieves itself catastrophically. Glass-makers avoid such catastrophes by "annealing" the glass, which means holding it for a long time at a high enough temperature that the molecules can move past each other but not too fast—in this way, the glass can find its way into a minimum-energy state where each molecule has had a chance to settle itself comfortably next to its neighbors with as little strain as possible, after which it can be completely cooled without problems. Systems in which elements interact with their neigh...

Conceptual Combination

Right now, as your eyes glide across this text, you are effortlessly understanding letters and words. How does your brain accomplish this remarkable feat, converting blobs of ink (or patterns of tiny pixels) into full-fledged ideas? Your brain uses concepts that you've accumulated throughout your lifetime. Each letter of the alphabet, each word, and each sequence of words that stands for an idea is represented in your brain by concepts. Even more remarkably, you can often comprehend things you've never seen before, like a brand new word in the middle of a sentence. You can see an unfamiliar breed of dog and still instantly know it's a dog. How does your brain achieve these everyday marvels? The answer is: concepts in combination. Most scientists will tell you that your brain contains a storehouse of concepts to categorize the objects and events around you. In this view, concepts are like dictionary definitions stored in your brain, such as "A pet is an animal companion that lives with ...

Exaptation

Some memes are fortunate at birth: they represent clear new concepts, are blessed with a memorable name, and have prominent intellectual "parents" who ably shepherd them through the crucial initial process of dissemination, clarification and acceptance. "Meme" itself is one of those lucky memes. Many other memes, however, are less fortunate in one or more of these respects, and through no fault of their own languish, for decades or even centuries, in the shadows of their highborn competitors. The core evolutionary concept of "change of function" is one of these unfortunate memes. It was one of Darwin's key intellectual offspring in The Origin—"the highly important fact that an organ originally constructed for one purpose... may be converted into one for a widely different purpose." It played a central role in Darwin's thinking about the evolution of novelty, particularly when a new function requires an already complex organ (e.g. lungs for breathing or wings for flying). But unlike it...

Verbal Overshadowing

Suppose that two people witness a crime: one describes in words what they saw, while the other does not. When tested later on their memories of the event, the person who verbally described the incident will be worse at later remembering or recognizing what actually happened. This is verbal overshadowing. Putting an experience into words can result in failures of memory about that experience, whether it be the memory of a person's face, the color of an object, or the speed that a car was going. This effect was discovered by the psychologist Elizabeth Loftus and her students in experiments exploring witness testimony and the malleability of human memory. The stakes are high. As Loftus has shown, imperfect memories can—and often do—put innocent people behind bars. Our memories define much of what we take to be real. Anything that interferes with memory interferes, effectively, with the truth. The idea that describing something in words can have a detrimental effect on our memory of it mak...

Standard Deviation

Suppose we choose an American woman at random. Given just a couple of numbers that we know characterize American women's heights, we can be 95% certain (meaning, we will be wrong only once out of every 20 times we do this) that her height will be between 4 feet 10 inches and 5 feet 10 inches. It is the statistical concept of standard deviation which allows us to say this. To show how, let us take such a data set: the heights of 1,000 randomly chosen American women, and let us plot this data as points on a graph where the x-axis shows height from 0 to 100 inches, and the y-axis shows the number of women who are of that height (we use only whole numbers of inches). If we then connect all these points into a smooth line, we will get a curve that is bell-shaped. Some data sets that have this characteristic shape, including this one, are said to have what is called a normal (also known as Gaussian) distribution, and it is the way in which a great many kinds of data are distributed. For data...

The Non-Returnable Universe

Thanks to online shopping, buying things now is much easier than before. You do not like something—you can always return it back for a full refund. A physicist might say that one can turn the arrow of time back for non-used purchases. A cosmologist may comment that we use a similar time reversal method in our research. Indeed, to understand the origin of the universe we may study its present evolution, and then solve the Einstein equations back in time. What we find is very similar to what happens then we play a movie back. At present, galaxies move away from each other. Playing the movie back shows them moving closer together. Going further back in time, we see that at some point the density of matter becomes infinitely large. This is the cosmological singularity. Solving the same equations forward in time, starting from the singularity, one finds that all matter appears from the singularity in a huge explosion, called the Big Bang. When the original cosmic fire cools down, matter con...

Mating Opportunity Costs

The concept of opportunity costs—the loss of potential gains from alternatives not chosen when a mutually exclusive choice must be made—is one of the most important concepts in the field of economics. But the concept is not well appreciated in the field of psychology. One reason for its absence is the sheer difficulty of calculating opportunity costs that occur in metrics other than money. Consider mate choice. Choosing one long-term mate means forgoing the benefits of choosing an available and interested alternative. But how are non-monetary benefits calculated psychologically? The complexities are multiple. The benefit-bestowing qualities of passed-over mates are many in number and disparate in nature. And there are inevitable tradeoffs among competing and incommensurate alternatives. Sometimes the choice is between a humorless mate with excellent future job prospects and a fun-loving mate destined for a low-status occupation; or between an attractive mate who c...

Galactic Centre

The development of meaning in cultural environment has been translated, regenerated, and repeated as well as in natural phenomena under the creative process in our life by compaction and expansion. The world of ousss is one of them. They have been developed throughout the public sector, private sector, scientific, literature and musical sector nevertheless that are only in ones poetric consequences. Society or a part of nature repeats by shrinking and collected power to grow and therefore the expansion would occur, like the plantation needs to make a gnarl to be grown and it needs to collect the complexity of the elements to make itself, following by the further growth of the branch. The middle age was one of the compaction where the depth of the pre renaissance was made, and the 20's historical immigration from the European countries to the united states flooded the uncountable quantity of the intellectual people's movement in America and this preconditioned to create most of the inv...

Herd Immunity

The eradication of smallpox was one of the most significant achievements of modern medicine. It was possible due to an effective vaccine, coupled with global vaccination programs. Theoretically, it is possible to eradicate other diseases such as measles or polio in a similar manner; if enough of the global population could be vaccinated, then these diseases would cease to exist. We have come tantalizingly close to eradication in some cases: In 2000, the Center for Disease Control and Prevention declared that measles had been eliminated from the United States. Sixteen years later, the Pan American Health Organization announced that measles had been eradicated from the Americas. Polio is now endemic in only three countries in the world. Infectious diseases that routinely killed young children are now preventable thanks to childhood vaccination programs. Yet despite these milestones, there have been several outbreaks of vaccine-preventable diseases in recent times. How can this be? A sig...

Positive Illusions

The human brain is built to say "no"; instead of "yes." We remember the negative. This "negativity bias," as psychologists call it, most likely evolved millions of years ago—perhaps primarily as an adaptive response to strangers who wandered into one's neighborhood. If our forebears greeted these foreigners with open arms, they might be slaughtered as they smiled. Long has natural selection favored those who responded negatively to the one malevolent intruder, rather than positively to myriad friendly guests. Even Ardi, a female relative who roamed the grass and forests of today's Ethiopia some 4.4 million years ago, had more to gain by fixating on the negative, rather than the positive. Today neuroscientists know where this negativity bias is located in the brain—largely in a neural region of the ventromedial prefrontal cortex, behind your forehead. This brain region becomes more active as you think negative thoughts. But as you overlook the negative and focus on the positive, activit...

Effect Size

The media are constantly looking for significant new discoveries to feed to the general public who want to know what controls our lives and how to better them. Cut down on salt, eat more vegetables, avoid social networking sites and so on, factors that have been reported to have significant effects on the health and welfare of individuals. Scientists also seek significance—though it is a technical term that has a different meaning to its common usage. In science, when a discovery is highly significant, it is one that is more likely to reflect a real state of Nature rather than a random fluctuation. However, when society hears that something is significant, this is interpreted as an important finding that has major impact. The problem is that patterns can be highly significant but not very meaningful to the individual. This is where effect size comes into play—a concept that ought to be more widely known. Calculating effect size (e.g. "Cohen's d") involves mathematics beyond the scope o...

The Climate System

The notion of a "climate system" is the powerful idea that the temperature we feel when we walk outside our door every day of the year, that the wind blowing on our faces while taking a walk, that the clouds we see in the sky, that the waves we watch rippling on the surface of the ocean as we walk along the beach, are all part of the same coherent, interconnected planetary system, governed by a small number of knowable, deterministic physical laws. The first explicit realization that planetary coherence is an attribute of many environmental phenomena we experience in our life probably coincided with the great explorations of the sixteenth and seventeenth century, when Halley—of comet fame—first postulated the existence of a general circulation of the atmosphere, from equator to poles, in response to differential heating of the planet by the sun. The reliability of the easterly winds, which ensured safe sailing westward on the great trade routes of the Atlantic, was a telling clue that ...

Media Richness

The term, "media richness," was first described in the context of media richness theory (MRT) by Richard Daft and Robert Lengel in 1986. Media richness describes the density of learning that can be conveyed through a specified communications medium. Face-to-face communication is the richest medium according to MRT because it allows for the simultaneous interpersonal exchange of cues from linguistic content, tone of voice, facial expressions, direction of gaze, gestures, and postures. MRT was developed prior to the rise of electronic communication media in order to help managers in business contexts decide which medium was most effective for communicating a message. Rich media like conversations and phone calls were deemed best for non-routine messages, while lean media like unaddressed memoranda were considered acceptable for routine messages. In the last two decades, media richness has been extended to describe the strengths and weaknesses of new media from email to websites, video co...

The Virial Theorem

The word "meme" denotes a rapidly spreading idea, behavior, or concept. Richard Dawkins originally coined the term to explain the action of natural selection on cultural information. For example, good parenting practices lead to children who survive to pass on those good parenting practices to their own children. Ask someone under twenty-five what a meme is, however, and chances are you will get a different definition: typing "meme" into Google Images yields page after page of photos of celebrities, babies, and kittens, overlaid with somewhat humorous text. Memes spread only as rapidly as they can reproduce. Parenting is a long-term and arduous task that takes decades to reproduce itself. A kitten photo reproduces in the few seconds it takes to resend. Consequently, the vast majority of memes are now digital, and the digital meaning of meme has crowded out its social and evolutionary meaning. Even in their digital context, memes are still usually taken to be a social phenomenon, selec...

Scaling

The word scale, when it refers to an object, may refer to a simple ruler. However, the act of measurement is the start of a deep relationship between geometry, physics and many important endeavors of humanity. Scaling, in the geometrical context, is the act of resizing an object while preserving certain essential characteristics such as its shape. It indicates a relationship that is robust under certain transformations. One uncovers scaling relationships by measuring and plotting key variables against each other. The simplest scaling relation is a linear one—yielding a straight line on a X-Y plot—denoting proportionality. The number of miles you can travel before refueling scales roughly linearly with the amount of fuel left in your gas tank. Twice the gas—double the miles that can be driven! More complicated scaling functions include power-laws, exponentials and so on each of which are reflective of the underlying spatial geometry or dynamics of the system. The circumference of a sphe...

Rheology

The world is governed by scientific principles that are fairly well taught and understood. A concept that resonates throughout physical science is rheology, and yet there are so few rheologists in academia that an international symposium fills only a small conference room. Rheo, coming from the Greek to flow, is primarily the study of how non-Newtonian matter flows. In practice, most rheologists look at how nanoparticles behave in complex compounds, often filled with graphene, silica, or carbon nanotubes. Rheology was key to the creation of tires and other polymer systems, but as new technologies incorporate flexible and stretchable devices for electronics, medical implants, regenerative and haptic garments for virtual reality experiences, rheologists will need to be as common as chemists. The primary reason for the relative obscurity of such an important topic is the hidden complexity involved. The number of connections in the human brain has been discussed by neuroscientists and ofte...

Positive Feedbacks in Climate Change

There is very little appreciation among the general public (and even among many scientists) of the great complexity of the mechanisms involved in climate change. Climate change significantly involves physics, chemistry, biology, geology, and astronomical forcing. The present political debate centers on the effect of the increase in the amount of carbon dioxide in the Earth's atmosphere since humankind began clearing the forests of the world and especially began burning huge quantities of fossil fuels, but this debate often ignores (or is unaware of) the complex climate system that this increase in carbon dioxide is expected to change (or not change, depending on one's political viewpoint). The Earth's climate has been changing over the 4.5 billion years of its existence. For at least the past 2.4 million years the Earth has been going through regular cycles of significant cooling and warming in the Northern Hemisphere that we refer to as ice age cycles. In each cycle there is a long gl...

Class Breaks

There's a concept from computer security known as a class break. It's a particular security vulnerability that breaks not just one system, but an entire class of systems. Examples might be a vulnerability in a particular operating system that allows an attacker to take remote control of every computer that runs on that system's software. Or a vulnerability in Internet-enabled digital video recorders and webcams that allow an attacker to recruit those devices into a massive botnet. It's a particular way computer systems can fail, exacerbated by the characteristics of computers and software. It only takes one smart person to figure out how to attack the system. Once he does that, he can write software that automates his attack. He can do it over the Internet, so he doesn't have to be near his victim. He can automate his attack so it works while he sleeps. And then he can pass the ability to someone—or to lots of people—without the skill. This changes the nature of security failures, and ...

The Scientific Method

There's a saying that there are no cultural relativists at thirty thousand feet. The laws of aerodynamics work regardless of political or social prejudices, and they are indisputably true. Yes, you can discuss to what extent they are an approximation, what are their limits of validity, do they take into account such niceties as quantum entanglement or unified field theory (of course they don't). But the most basic scientific concept that is clearly and disturbingly missing from today's social and political discourse is the concept that some questions have correct and clear answers. Such questions can be called "scientific" and their answers represent truth. Scientific questions are not easy to ask. Their answers can be verified by experiment or observation, and they can be used to improve your life, create jobs and technologies, save the planet. You don't need pollsters or randomized trials to determine if a parachute works. You need an understanding of the facts of aerodynamics and th...

Prediction Error Minimization

This sounds dry and technical. But it may well be the key thing that brains do that enables us to experience a world populated by things and events that matter to us. If so, it is a major part of the solution to the mind-body problem itself. It is also a concept that can change how we feel about our own daily experience. Brains like ours, if recent waves of scientific work using this concept are on track, are fundamentally trying to minimize errors concerning their own predictions of the incoming sensory stream. Consider something as commonplace as it is potentially extremely puzzling—the capacity of humans and many other animals to find specific absences salient. A repeated series of notes, followed by an omitted note, results in a distinctive experience—it is an experience that presents a world in which that very note is strikingly absent. How can a very specific absence make such a strong impression on the mind? The best explanation is that the incoming sensory stream is processed r...

Emergence

Thought, passion, love... this internal world we experience, including all the meaning and purpose in our lives, arises naturally from the interactions of elementary particles. This sounds absurd, but it is so. Scientists have attained a full understanding of all fundamental interactions that can happen at scales ranging from subatomic particles to the size of our solar system. There is magic in our world, but it is not from external forces that act on us or through us. Our fates are not guided by mystical energies or the motions of the planets against the stars. We know better now. We know that the magic of life comes from emergence. It is the unimaginably large numbers of interactions that make this magic possible. To describe romantic love as the timely mutual squirt of oxytocin trivializes the concerted dance of more molecules than there are stars in the observable universe. The numbers are beyond astronomical. There are approximately 100 trillion atoms in each human cell, and abou...

It's About Time

Time is a scientific concept that deserves greater thought and study, though, despite advancements in the mathematical behaviors of time over long horizons under what I would call extreme conditions, it is a concept we will never be positioned to properly understand. Time is not simply a matter of duration; time is movement, motion, transition and change. It's not static, to be ticked off, eliminated. If we consider one of the best known implications of e=mc2, time is relative, it depends upon perspective. Black holes, as hungry-hippos of matter, could be considered a waste of time. Some say time flies when you're having fun, lending colloquial truth to the notion time is relative. There are boundaries to time in the temporal/spatial sphere just as there are in the sphere of neuro-chemical subjectivity. Time varies according to experience, perception of pain, focus, thought or its absence. Meditation can make time meaningless. Mindlessness, in a sense, does away with time, just as e...

The Brainstem

Today, neuro-biology provides increasing evidence of how our reason, although powerful, isn't as constant as most social scientists assume. Now we know that inner brain areas related to homeostatic and basic physiological functions are more relevant and permanent for surviving and evolving, than external areas of the cortex related to cognitive faculties. Complex cognitive skills do enrich our mental life, but aren't critical for regulating physiological functions that are basic for existing. In a sense, we can exist with a poorer mental life—for instance following a damage in our external cortex, but we can't exist without the basic regulation of our heartbeat or the respiratory rhythm-for instance, following a damage in our Brainstem. In fact, as Antonio Damasio has already explained, the Brainstem potentially houses the origin of consciousness—the complex mental representation of the "self" that we continuously experience in first person. Even slight damages in subareas of the Bra...

General Standardization Theory

Try building a tower by piling irregular stones on top of each other. It can be done, eight, nine, sometimes ten stones high. You need a stable hand and a good eye to spot each rock's surface features. You find such man-made "Zen stone towers" on riverbanks and mountaintops. They last for a while until the wind blows them over. What is the relationship here between skill and height? Take relatively round stones from a riverbank. A child of two can build a tower two stones high. A child of three with improved hand-eye-coordination can manage three stones. You need experience to get to eight stones. And you need tremendous skill and a lot of trial and error to go higher than ten. Dexterity, patience and experience can get you only so far. Now, try with a set of interlocking toy bricks as your stones. You can build much higher. More importantly: your three-year-old can build as high as you can. Why? Standardization. The stability comes from the standardized geometry of the parts. The adva...

Ashby's Law of Requisite Variety

W. Ross Ashby was a British cybernetician working in the 1950s who became interested in the phenomenon of homeostasis—the way in which complex systems operating in changing environments succeed in maintaining critical variables (for example, internal body temperature in biological systems) within tightly-defined limits. Ashby came up with the concept of variety as a measurement of the number of possible states of a system. His "Law" of Requisite Variety stated that for a system to be stable, the number of states that its control mechanism is capable of attaining (its variety) must be greater than or equal to the number of states in the system being controlled. Ashby's Law was framed in the context of his interest in self-regulating biological systems, but it was rapidly seen as having a relevance for other kinds of systems. The British cybernetician and operational research practitioner Stafford Beer, for example, used it as the basis for his concept of a viable system in organizationa...

Russell Conjugation

We are told that we are entitled to our own opinions but not our own facts. This leaves out the observation that the war for our minds and attention is now increasingly being waged over neither facts nor opinions, but feelings. In an era in which anyone can publish anything, the quest to control information has largely been lost by institutions, with a race on to weaponize empathy by understanding its basis in linguistics and tweaking the social media algorithms which now present our world to us accordingly. As the theory goes, it is not that we don't have our own opinions so much as that we have too many contradictory ones, and it is generally our emotional state alone which determines on which ones we will predicate action or inaction. Russell Conjugation (or "emotive conjugation") is a presently obscure construction from linguistics, psychology and rhetoric which demonstrates how our rational minds are shielded from understanding the junior role factual information generally plays r...

De-Anonymization

We keep hearing about Big Data as the latest magic solution for all society's ills. The sensors that surround us collect ever more data on everything we do; companies use it to work out what we want and sell it to us. But how do we avoid a future where the secret police know everything? We're often told our privacy will be safe, because our data will be made anonymous. But Dorothy Denning and other computer scientists discovered in about 1980 that anonymization doesn't work very well. Even if you write software that will only answer a query if the answer is based on the data of six or more people, there's a lot of ways to cheat it. Suppose university professors' salaries are confidential, but statistical data are published, and suppose that one of the seven computer science professors is a woman. Then I just need to ask "Average salary computer science professors?" and "Average salary male computer science professors?" And given access to a database of "anonymous" medical records, I ca...

Social Identity

We know we are ultra-social animals and yet have a consistent blind spot about how truly social we are. Our naïve realism leans us toward a self-image as individual, atomistic rational agents experiencing life as though peering out on the world through a window. And like the fish that swims unaware of the water in which it is suspended, we struggle to see the social reality in which our actions are meaningfully conducted. Contrary to this view, psychology has shown repeatedly how deeply permeated each of us is by a social identity. This is an important corrective to our illusory self-image and gives us a better insight into our social natures. But even where our social identity has entered the picture it is often crucially misunderstood. Social identity has been explored in earnest ever since the Second World War in an attempt to understand how it was possible for ordinary people to commit, or at least to allow, genocidal horrors. Much of this work has suggested, such as the Milgram ex...

Substrate-Independence

What do waves, computations and conscious experiences have in common, that provides crucial clues about the future of intelligence? They all share an intriguing ability to take on a life of their own that's rather independent of their physical substrate. Waves have properties such as speed, wavelength and frequency, and we physicists can study the equations they obey without even needing to know what substance they are waves in. When you hear something, you're detecting sound waves caused by molecules bouncing around in the mixture of gases we call air, and we can calculate all sorts of interesting things about these waves—how their intensity fades as the square of the distance, how they bend when they pass through open doors, how they reflect off of walls and cause echoes, etc.—without knowing what air is made of. We can ignore all details about oxygen, nitrogen, carbon dioxide, etc., because the only property of the wave's substrate that matters and enters into the famous wave equat...

Enactivism

What exactly do brains do? The usual answer is that they form mental representations of the world on the far side of the skull. Brains, that is, create internal virtual worlds—their best or most useful simulations of the real external world, one which exists independently of any of them but within which they all reside. The problem, however, is that fundamental physics denies the existence of this observer-independent world. From quantum physics in the early 20th century to the black hole firewall debate that rages today, physicists have found that we tangle ourselves in paradox and violate laws of physics when we attempt to compile multiple viewpoints into a single spacetime. The state of a physical system, we've learned, can only be defined relative to a given observer. (Here "observer" does not mean consciousness, but a physical system capable of acting as a measuring device—yet one that itself must enjoy only a relational existence.) Slices of spacetime accessed by different observ...

PT Symmetry

When Dirac formulated the postulates of quantum theory, he required Hermiticity to be the fundamental symmetry for his equations. For Dirac, the requirement of Hermiticity was the mathematical device that he needed to ensure that all predictions for the outcomes of real-world measurements of quantum systems resulted in a real number. This is important since we only observe real outcomes in actual experimental observations. Dirac's choice of Hermiticity as the fundamental symmetry of quantum theory was not seriously challenged for around seventy years. Hermiticity is a subtle and abstract symmetry that is mathematical in its origin. Broadly speaking, the requirement of Hermiticity imposes a boundary on a system. This is an idealization in which a system is isolated from any surrounding environment (and hence cannot be measured). While this gives a tractable mathematical framework for quantum theory, it is an unphysical requirement since all systems interact with their environment and ...

Mental Emulation

When he was sixteen years old, Albert Einstein imagined that he was chasing after a beam of light and observed what he "saw." And this vision launched him on the path to developing his theory of special relativity. Einstein often engaged in such thinking; he reported: "...The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined... this combinatory play seems to be the essential feature in productive thought before there is any connection with logical construction in words or other kinds of signs which can be communicated to others..." Einstein was relying on mental emulation, a kind of thought that many of us use and we all probably could use more frequently—and more productively—if we become aware of it. Mental emulations range from the sublime to the ordinary, such as imagining currently impossible events (including chasing after a beam of light), or imagining the best route to t...

Blind Analysis

When we measure a value that is consistent with the prediction our tendency is to trust the result. When we get an unexpected answer we apply greater scrutiny, trying to determine if we've made an error before believing the surprise. This tilts us toward revealing errors in one category of measurements and leaving them unexposed in another. It is particularly dangerous when our assumptions are flawed—and if there is anything we should bet on, given the history of progress within physics, it's that our underlying assumptions are in some way flawed. Bias can creep into the scientific process in predictable and unpredictable ways. Blind analyses are employed as a protection against bias. The idea is to fully establish procedures for a measurement before we look at the data so we can't be swayed by intermediate results. They require rigorous tests along the way to convince ourselves that the procedures we develop are robust and that we understand our equipment and techniques. We can't "un...

Replicator Power

Where does all the design in the universe come from? Around me now, and indeed almost everywhere I go, I see a mixture of undesigned and designed things: rocks, stars and puddles of rain; tables, books, grass, rabbits and my own hands. The distinction between designed and undesigned is not commonly made this way. Typically people are happy to divide rocks from books on the grounds that rocks were not designed for a function while books were. Books have an author, a publisher, a printer, and a cover designer, and that means "real" top-down design. As for grass, rabbits and hands—they do serve functions but they evolved through a mindless bottom-up process, and that is not "real" design. This other distinction between real design and evolved "design" is sometimes explicitly stated, but even when it's not, the fear of attributing design to a mindless process is revealed in the scare quotes that evolutionary biologists sometimes put around that word "design." Eyes are brilliantly "desi...

Functional Equations

Where does mathematics come from? I'm not talking about the philosophical question of whether mathematical truths have an existence independent of human minds. I mean concretely. What on earth is this field? When a mathematician makes cryptic pronouncements like, "We define the entropy of a probability distribution to be such-and-such," who or what led them to explore that definition over any other? Are they accepting someone else's definition? Are they making up the definition themselves? Where exactly does this whole dance begin? Mathematics textbooks contain a mixture of the timeless and the accidental, and it isn't always easy to tell exactly which bits are necessary, inevitable truths, and which are accidental social constructs that could have easily turned out differently. An anthropologist studying mathematicians might notice that, for some unspecified reason, this species seems to prefer the concept of "even numbers" over the barely distinguishable concept of "(s?)even numbers...

Intellectual Honesty

Wherever we look, we find otherwise sane men and women making extraordinary efforts to avoid changing their minds. Of course, many people are reluctant to be seen changing their minds, even though they might be willing to change them in private, seemingly on their own terms—perhaps while reading a book. This fear of losing face is a sign of fundamental confusion. Here it is useful to take the audience's perspective: Tenaciously clinging to your beliefs past the point where their falsity has been clearly demonstrated does not make you look good. We have all witnessed men and women of great reputation embarrass themselves in this way. I know at least one eminent scholar who wouldn't admit to any trouble on his side of a debate stage were he to be suddenly engulfed in flames. If the facts are not on your side, or your argument is flawed, any attempt to save face is to lose it twice over. And yet many of us find this lesson hard to learn. To the extent that we can learn it, we acquire a su...

Genetic Rescue

Wildlife populations are most threatened when their numbers become reduced to the point that their genetic diversity is lost. Their narrowing gene pool can accelerate into what is called an "extinction vortex." With ever fewer gene variants (alleles), the ability to adapt and evolve declines. As inbreeding increases, deleterious genes accumulate, and fitness plummets. The creatures typically have fewer offspring, many of them physically or behaviorally impaired, susceptible to disease, increasingly incapable of thriving. Most people assume they are doomed, but that no longer has to be what happens. "Genetic rescue" restores genetic diversity. Conservation biologists are warming to its use with growing proof of its effectiveness. One study of 156 cases of genetic rescue showed that 93% had remarkable success. The most famous case was a dramatic turnaround for the nearly extinct Florida panther. By the mid-1990s only 26 were left, and they were in bad shape. In desperation, conservationi...

Transfer Learning

You can never understand one language until you understand at least two. This statement by the English writer, Geoffrey Willans, feels intuitive to anyone who has studied a second language. The idea is that learning to speak a foreign language inescapably conveys deeper understanding of one's native language. Goethe, in fact, found this such a powerful concept that he felt moved to make a similar, but more extreme, assertion: He who does not know foreign languages does not know anything about his own. As compelling as this may be, what is perhaps surprising is that the essence of this idea—that learning or improvement in one skill or mental function can positively influence another one—is present not only in human intelligence, but also in machine intelligence. The effect is called transfer learning, and besides being an area of fundamental research in machine learning, it has potentially wide-ranging practical applications. Today, the field of machine learning, which is the scientific...

Decentering

You may have worked so closely with a partner that you reached a point where each of you could finish the other's sentences. You had a pretty good idea of how your partner would respond to an event. What's behind such a skill? Decentering is the activity of taking the perspective of another entity. When we look into the past, we try to explain why that entity behaved in a way that might have surprised us. Peering into the future, we decenter in order to anticipate what that entity is likely to do. Skilled decentering comes into play, not just with partners, but also with strangers and even with adversaries. It gives us an edge in combat, to get ready to ward off an adversary's attack. It helps authors write more clearly as they anticipate what might confuse a reader or what a reader expects to find out next. Police officers who are good at decentering can de-escalate a tense situation by moving an encounter into less volatile directions. Teachers rely on decentering to keep the atten...

Humility

You might not think of humility as a scientific concept, but the special brand of humility that is enshrined in scientific culture is deserving of special recognition for its unique heuristic transformative power. I reflect upon Sir Richard Southwood's invitation an incoming class of Oxford undergraduate biologists: "Remember, perhaps 50% of the facts that you learn may be not be quite right, or even wrong! It is your job to find out where new ideas are needed." In the scientist's toolkit of concepts for solving problems, scientific humility is among the most useful tool for finding the better pathway. It clarifies, it inspires, and it should be more widely known, practiced, and defended. Respect for scientific humility gives us license to question in ways all too rare in other professional fields. Allow yourself to ponder: When were you last surprised? When were you last wrong? As scientists, we are explorers and need to wonder and play. We need to have ample freedom to tinker and f...

Isolation Mismatch

You won't find the term "isolation mismatch" in any scientific dictionary. Isolation mismatches occur when two complex adaptive systems cannot be merged after evolving in isolation from each other. It is a generalization of a concept that you might find in a scientific dictionary, "Dobzhansky-Muller incompatibilities," which cause isolated biological populations to become separate species. When ported into the realm of culture, isolation mismatches might explain how cultures (not species) can diverge and become incompatible. It might also account for our disconcerting human tendencies towards xenophobia or fear of other human cultures. But let's consider biology first, then the cultural analogy. Formation of new biological species usually involves isolation and independent evolution of the two populations. As one toad population evolves through natural selection, each of its novel genes is tried out in many toads and will necessarily be selected to work together with the other genes in...

Babylonian Lottery

"Like all men in Babylon, I have been procounsel; like all, a slave"— Jorge Luis Borges, Lottery in Babylon The lottery in Babylon begins as a simple game of chance. Tickets are sold, winners are drawn, a prize awarded. Over time, the game evolves. Punishments are doled out alongside prizes. Eventually the lottery becomes compulsory. Its cadence increases, until the outcomes of its drawings come to underpin everything. Mundane events and life turns are subject to the lottery's "intensification of chance." Or perhaps, as Borges alludes, it is the lottery's explanatory power that grows, as well as that of its shadowy operator the Company, until all occurrences are recast in light of its odds. Babylonian Lottery is a term borrowed from literature, for which no scientific term exists. It describes the slow encroachment of programmatic chance, or what we like to refer to today as "algorithms." Today as in Babylon, we feel the weight of these algorithms. They amplify our product choices and ...

The Neural Code

"Neural code" is by far the most under-appreciated term, and concept, in science. It refers to the rules or algorithms that transform action potentials and other processes in the brain into perceptions, memories, meanings, emotions, intentions, and actions. Think of it as the brain's software. The neural code is science's deepest, most consequential problem. If researchers crack the code, they might solve such ancient philosophical mysteries as the mind-body problem and the riddle of free will. A solution to the neural code could also give us unlimited power over our brains and hence minds. Science fiction—including mind control, mind reading, bionic enhancement and even psychic uploading—will become reality. Those who yearn for the Singularity will get their wish. More than a half-century ago, Francis Crick and others deciphered the genetic code, which underpins heredity and other biological functions. Crick spent his final decades seeking the neural code—in vain, because the most pro...

Non Ergodic

"Non ergodic" is a fundamental but too little known scientific concept. Non-ergodicity stands in contrast to "ergodicity. "Ergodic" means that the system in question visits all its possible states. In Statistical Mechanics this is based on the famous "ergodic hypothesis, which, mathematically, gives up integration of Newton's equations of motion for the system. Ergodic systems have no deep sense of "history." Non-ergodic systems do not visit all of their possible states. In physics perhaps the most familiar case of a non-ergodic system is a spin glass which "breaks" ergodicity and visits only a tiny subset of its possible states, hence exhibits history in a deep sense. Even more profoundly, the evolution of life in our biosphere is profoundly "non-ergodic" and historical. The universe will not create all possible life forms. This, together with heritable variation, is the substantial basis for Darwin, without yet specifying the means of heritable variation, whose basis Darwin did not k...

Determinism

A concept that everyone should understand and appreciate is the idea of physical determinism: that all matter and energy in the universe, including what's in our brain, obey the laws of physics. The most important implication is that is we have no "free will": At a given moment, all living creatures, including ourselves, are constrained by their genes and environment to behave in only one way—and could not have behaved differently. We feel like we make choices, but we don't. In that sense, "dualistic" free will is an illusion. This must be true from the first principles of physics. Our brain, after all, is simply a collection of molecules that follow the laws of physics; it's simply a computer made of meat. That in turn means that given the brain's constitution and inputs, its output—our thoughts, behaviors and "choices"—must obey those laws. There's no way we can step outside our mind to tinker with those outputs. And even molecular quantum effects, which probably don't even affect ou...

Morphogenetic Field

A morphogenetic field is a region of an embryo that forms a discrete structure, such as a limb or heart. Morphogenetic fields became known through the experimental work of Ross G. Harrison, one of the most deserving scientists never to have won a Nobel Prize. The regions are described as fields instead of discrete cells because they can recover from the effects of partial destruction. For example, if half of a salamander's forelimb field is destroyed, it will still develop into a reasonable approximation of a complete limb, not a half-limb. If the limb field is transplanted to a novel region, such as the mid-flank of a host embryo, it will develop into an extra limb. These remarkable and still valid discoveries were widely reported in the scientific and popular media during the Golden Age of experimental embryology in the first half of the 20th century, but have been partially eclipsed by the emergence of more modern, reductionistic approaches to developmental problems. The morphogenet...

Fundamental Attribution Error

Aristotle taught that a stone sinks when dropped into water because it has the property of gravity. Of course, not everything sinks when dropped into water. A piece of wood floats, because it has the property of levity. People who behave morally do so because they have the property of virtue; people who don't behave morally lack that property. Molière lampoons this way of thinking by having a team of physicians in The Imaginary Invalid explain why opium induces sleep, namely because of its dormative power. Lampoon or not, most of us think about the behavior of objects and people much of the time in purely dispositional terms. It is properties possessed by the object or person that explain its behavior. Modern physics replaced Aristotle's dispositional thinking by describing all motion as being due to the properties of an object interacting in particular ways with the field in which it is located. Modern scientific psychology insists that explanation of the behavio...

The Premortem

Before a major decision is taken, say to launch a new line of business, write a book, or form a new alliance, those familiar with the details of the proposal are given an assignment. Assume we are at some time in the future when the plan has been implemented, and the outcome was a disaster. Write a brief history of that disaster. Applied psychologist Gary Klein came up with "The Premortem," which was later written about by Daniel Kahneman. Of course we are all too familiar with the more common postmortem that typically follows any disaster, along with the accompanying finger pointing. Such postmortems inevitably suffer from hindsight bias, also known as Monday-morning quarterbacking, in which everyone remembers thinking that the disaster was almost inevitable. As I often heard Amos Tversky say, "the handwriting may have been written on the wall all along. The question is: was the ink invisible?" There are two reasons why premortems might help avert disasters. (I say might because I ...

Bisociation

Charles Lamb once remarked that, when the time came for him to leave this earth, his fondest wish would be to draw his last breath through a pipe and exhale it in a pun. And he was indeed a prodigious punster. Once, when a friend, about to introduce the notoriously shy English essayist to a group of strangers, asked him, "Promise, Lamb, not to be so sheepish," he replied, "I wool." Lamb and his close friend Samuel Taylor Coleridge shared a passion for punning, not just as a fireside diversion but as a model for the way the imaginative mind works. "All men who possess at once active fancy, imagination, and a philosophical spirit, are prone to punning," Coleridge declared. Coleridge considered punning an essentially poetic act, exhibiting sensitivity to the subtlest, most distant relationships, as well as an acrobatic exercise of intelligence, connecting things formerly believed to be unconnected. "A ridiculous likeness leads to the detection of a true analogy" is the way he explained it...

Complementarity

Complementarity is the idea that there can be different ways of describing a system, each useful and internally consistent, which are mutually incompatible. Complementarity first emerged as a surprising feature of quantum theory, but I, following Niels Bohr, believe it contains wisdom that is much more widely applicable. Here's how it works in quantum theory: The ultimate description of a system is its wave function, but the wave function is not something we can observe directly. It is like a raw material, which must be processed and sculpted in order to build something usable (i.e., observable). There are many things we might choose to build from a lode of iron ore—a sword or a plowshare, for example. Both might be useful, in different circumstances. But either uses up the raw material, and precludes building the other. Similarly, we can process the wave function of a particle to predict things about its position, or alternatively to predict things about its velocity, but not both ...

The Principle of Least Action

Complexity makes life interesting. A universe of just Hydrogen is quite bland, but the helpful production of Carbon in stellar cores allows for all kinds of chemical connections. A universe of just two dimensions is pretty limited, but live in at least three and enjoy the greater range of motion and possible spatial permutations. Sitting on a bench in my friend's garden in California, there's a lot to look at. The visual information filling my field of view is incredibly complicated. The dry winter leaves trace vortices in the air's motion. Plants respire and we breathe and the neural connections fire and it's all complex and interesting. The physicist's job is to see through the overwhelming intricacy and find the rallying, organizing principle. Everything in this garden, from the insects under the rocks to the blue dome overhead to the distant stars washed out by the sunlight can be traced to a remarkably lean origin in a big bang. Not to overstate the case. There's much we don't ...

The Schnitt

For all our scientific efforts, there remains a gap, the Schnitt. The gap between the quantum and the classical, between the living and the non-living, between the mind and the brain. How on earth is science going to close this gap, what the physicist Werner Heisenberg called the Schnitt, and what the theoretical biologist Howard Pattee calls the "epistemic cut"? Some maintain the gaps only reflect a current failure of knowledge. Others think the gaps will never be closed, that they are in fact un-closeable. Pattee, who has been working at the problem for fifty years, believes he has a handle on it. I think he does too. The clue to grasping his idea goes all the way back to understanding the difference between non-living and living systems. To understand this difference, biologists need to fully embrace the gift from modern physics, the idea of complementarity. Accepting this unexpected gift is not easy. Einstein himself wouldn't accept it until Niels Bohr forced him to. The discovery ...

Antisocial Preferences

For at least fifty years, the rational self-interested agent of neoclassical economics, Homo economicus, has been questioned, rebutted, and in some cases disparaged as a model psychopath. A seminal critique appeared in 1968 with the publication of Garrett Hardin's article, "The Tragedy of the Commons." Hardin invited the reader to consider a pasture open to all neighboring herdsman. If those herdsmen pursued their own rational self-interest, he reasoned they would continue to add cows to their herds, ultimately leading to the pasture's destruction. This has the structure of a multi-player Prisoner's Dilemma wherein the individual pursuit of rational self-interest inevitably leads to social catastrophe. Contrary to Homo economicus, people appear to care about more than their own material payoffs. They care about fairness and appear to care about the positive welfare of others. They possess what economists refer to as social preferences. In Dictator games, for example, a person is given ...

Reciprocal Altruism

For societies to survive and thrive, some significant proportion of their members must engage in reciprocal altruism. All sorts of animals, including humans, will pay high individual costs to provide benefits for a non-intimate other. Indeed, this kind of altruism plays a critical role in producing cooperative cultures that improve a group's welfare, survival, and fitness. The initial formulation of reciprocal altruism focused on a tit-for-tat strategy in which the altruist expected a cooperative response from the recipient. Game theorists posit an almost immediate return (albeit iterated), but evolutionary biologists, economists, anthropologists, and psychologists tend to be more concerned with returns over time to the individual or, more interestingly, to the collective. Evidence is strong that for many human reciprocal altruists the anticipated repayment is not necessarily for the person who makes the initial sacrifice or even for their family members. By creating a culture of co...

Scientific Realism

Has science discovered the existence of protons and proteins, neurons and neutrinos? Have we learned that particles are excitations of underlying quantum fields and that the transmission of inherited characteristics is accomplished by way of information-encoding genes? Those who answer no (as opposed to dunno) probably aren't unsophisticated science deniers. More likely they're sophisticated deniers of scientific realism. Scientific realism is the view that science expands upon—and sometimes radically confutes—the view of the world that we gain by means of our sense organs. Scientific theories, according to this view, extend our grasp of reality beyond what we can see and touch, pulling the curtain of our corporeal limitations aside to reveal the existence of whole orders of unobserved and perhaps unobservable things, hypothesized in order to explain observations and having their reference fixed by the laws governing their behavior. In order for theories to be true (or at any rate, app...

Gravitational Radiation

Humans as well as most other mammals detect, from birth onward, electromagnetic radiation in the form of visible light. But it was not until the 1887 experiments by Heinrich Hertz that scientists accepted that what they were seeing was nothing but a frequency band of the electromagnetic radiation generated by accelerating electric charges. These experiments confirmed the prediction James Clerk Maxwell had made less than three decades earlier. The realization opened the door to studying electromagnetic radiation of all frequencies, from radio waves to X-rays and beyond. It also stimulated scientists to ask if an entirely different form of radiation might ever possibly be observed. Accelerating masses rather than electric charges would be its source and it would be called gravitational radiation. Maxwell's equations had shown what form electromagnetic radiation would take. Albert Einstein's 1916 general theory of relativity offered a prediction for gravitational radiation. But since the ...

Neurodiversity

Humans have diversity in neurological conditions. While some, such as autism are considered disabilities, many argue that they are the result of normal variations in the human genome. The neurodiversity movement is an international civil rights movement that argues that autism shouldn't be "cured" and that it is an authentic form of human diversity that should be protected. In the early 1900s eugenics and the sterilization of people considered genetically inferior were scientifically sanctioned ideas, with outspoken advocates like Theodore Roosevelt, Margaret Sanger, Winston Churchill and US Supreme Court Justice Oliver Wendell Holmes Jr. The horror of the Holocaust, inspired by the eugenics movement, demonstrated the danger and devastation these programs can exact when put into practice. Temple Grandin, an outspoken spokesperson for autism and neurodiversity argues that Albert Einstein, Wolfgang Mozart and Nikola Tesla would have been diagnosed on the "autistic spectrum" if they ha...

Liminality

I am writing this on the winter solstice. At 5.44am Eastern Standard Time I stood on a porch in Vermont and watched the sky. Nothing to discern that was tangible. But somewhere at ancient sites light passed over etched rock. Over millennia, ancient people such as those once here on the banks of the Connecticut River, marked a transition. The science is there for the shortest day. But what emerges for me is a search for absolute acuteness: that nano point where some thing changes, and every thing changes. So, I am excited by liminality. At a time which celebrates fuzziness and mergings and convergence I am also intrigued by that absolute movement from one stage to another, one which finesses so acutely, it has a point. My concept to celebrate comes out of social science, but is mediated by ethnography and anthropology, archaeology too in the tangible remainders of transition. My motherlode is "Rites of Passage" or "Les Rites du Passage" by the prehistorian and ethnographer, Arnold Van G...

Costly Signalling

If something doesn't make sense, your go-to hypothesis should be "costly signalling." The core idea is more than a century old, but new wrinkles deserve wider exposure. Veblen's "conspicuous consumption" explained why people lit their cigars with $100 bills as a costly signal of their wealth. Later economists showed that a signal of a hidden trait becomes reliable if the cost of faking it is more than the expected gain. For example, Spence showed that college degrees (even in irrelevant subjects) can reliably signal good future employees because they are too costly for bad employees to obtain. Darwin said, "The sight of a feather in a peacock's tail, whenever I gaze at it, makes me sick!" because he couldn't see its adaptive benefit. It makes perfect sense as a costly signal, however, because the peacock has to be quite fit to survive with a tail like that! Why do strong gazelles waste time and energy "stotting" (jumping vertically) when they see a cheetah? That is a costly signal of t...

Deliberate Ignorance

Ignorance is generally pictured as an unwanted state of mind, and the notion of deliberate ignorance may raise eyebrows. Yet people often choose to be ignorant, demonstrating a form of negative curiosity at odds with concepts such as ambiguity aversion, a general need for certainty, and the Bayesian principle of total evidence. Such behavior also contrasts with the standard belief that more knowledge and data are always preferred, expressed in various forms from Aristotle ("All men by nature desire to know") to the view of humans as informavores to the mission of national surveillance programs. Deliberate ignorance can be defined as the willful decision not to know the answer to a question of personal interest, even if the answer is free, that is, with no search costs. The concept differs from the study of agnotology or the sociology of ignorance, which investigate the systematic production of ignorance by deflecting, covering up, and obscuring knowledge, such as the tobacco industry's...

Life History

Imagine that an Alpha Centauran scientist came to Earth 150,000 years ago. She might note, in passing, that the newly evolved Homo sapiens were just a little better at tool use, cooperation, and communication than their primate relatives. But, as a well-trained evolutionary biologist, she would be far more impressed by their remarkable and unique "life history." "Life history" is the term biologists use to describe how organisms change over time—how long an animal lives, how long a childhood it has, how it nurtures its young, how it grows old. Human life history is weird. We have a much longer childhood than any other primate—twice as long as chimps, and that long childhood is related to our exceptional learning abilities. Fossil teeth suggest that this long childhood evolved in tandem with our big brains—we even had a longer childhood than Neanderthals. We also rapidly developed special adaptations to care for those helpless children—"pair-bonding" and "alloparents." Fathers and unrel...

Simulated Annealing

Imagine you are very nearsighted, so that you can see only the region locally near you, but can observe nothing globally, far away. Now imagine you are situated at the top of a mountain, and you want to make your way down by foot to the lowest point in the valley. But you cannot see beyond your feet, so your algorithm is simply to keep heading downhill, wherever gravity takes you fastest. You do that, and eventually, half way down the mountain, you end up at the bottom of a small oval ditch or basin, from which all paths lead up. As far as you can nearsightedly tell, you've reached the lowest point. But it's a local minimum, not truly the bottom of the valley, and you're not where you need to be. What would be a better algorithm for someone with purely local vision? Simulated annealing, inspired by sword makers. To make a metal sword, you have to first heat the metal until it's hot and soft enough to shape or mold. The trouble is that when the metal subsequently cools and crystallize...

The Law of Small Numbers

In 1832, a Prussian military analyst named Carl von Clausewitz explained that "three quarters of the factors on which action in war is based are wrapped in a fog of . . . uncertainty." The best military commanders seemed to see through this "fog of war," predicting how their opponents would behave on the basis of limited information. Sometimes, though, even the wisest generals made mistakes, divining a signal through the fog when no such signal existed. Often, their mistake was endorsing the law of small numbers—too readily concluding that the patterns they saw in a small sample of information would also hold for a much larger sample. Both the Allies and Axis powers fell prey to the law of small numbers during World War II. In June 1944, Germany flew several raids on London. War experts plotted the position of each bomb as it fell, and noticed one cluster near Regent's Park, and another along the banks of the Thames. This clustering concerned them, because it implied that the German mi...

Menger Sponge

In the 2006 Taiwanese thriller movie Silk, a scientist creates a Menger Sponge, a special kind of hole-filled cube, to capture the spirit of a child. The Sponge not only functions as an anti-gravity device but seems to open a door into a new world. As fanciful as this film concept is, the Menger Sponge considered by mathematicians today is certainly beautiful to behold, when rendered using computer graphics, and a concept that ought to be more widely known. Certainly, it provides a wonderful gateway to fractals, mathematics, and reasoning beyond the limits of our own intuition. The Menger Sponge is a fractal object with an infinite number of cavities—a nightmarish object for any dentist to contemplate. The object was first described by Austrian mathematician Karl Menger in 1926. To construct the sponge, we begin with a mother cube and subdivide it into twenty-seven identical smaller cubes. Next, we remove the cube in the center and the six cubes that share faces with it. This leave...

Regression to the Mean

In this somber time, asking what scientific term or concept ought to be more widely known sounds like the setup for a punchline, something like "2+2=4" or "to every action there is an equal and opposite reaction." We can make a joke like that, but the truth the joke reveals is that "science" is indeed very much a human conception and construction. Science is all in our minds, even as we see dramatic examples of the use of that science all around us. So this year's question is really a question about where to begin: What is there that we should all know that we don't know as well as we should, don't apply to our everyday and extraordinary challenges as tellingly as we could, and don't pass on to children in nursery rhymes and the like? My candidate is an old, simple, and powerful one: the law of regression to the mean. It's a concept from the discipline of statistics, but in real life it means that anomalies are anomalies, coincidences happen (all the time, with stunning freq...

Referential Opacity

It is commonly assumed that when people make a free choice in an election, the outcome will be what those on the winning side intended. But there are two factors known to cognitive science—but probably not known to politicians—which may well render this assumption false. The first is the fact of "referential opacity," as it applies to mental states. A peculiar characteristic of mental states—such as believing, wanting, remembering—is that they do not conform to Leibniz's law. This law states that if two things, A and B, are identical, then in any true statement about A, you can replace A by B, and the new statement will also be true. So, if it's true A weighs five kilos, it must be true B weighs five kilos, if it's true A lives in Cambridge, it must be true B lives in Cambridge, and so on. The strange thing is however, that, when it comes to mental states, this substitution no longer works. Suppose, for example, the Duke of Clarence and Jack the Ripper were one and the same person. It ...

Exponential

It is not clear whether it was rice or wheat. We're also not sure of the origin of the story, for there are many versions. But it goes something like this: A king was presented with a beautiful game of chess by its inventor. So pleased was the king that he asked the inventor to name his own reward. The inventor modestly asked for some rice (or wheat). The exact quantity would be calculated through the simplest formula: put a grain on the first square, two on the second, four on the third, and so on doubling the number of grains until the sixty-fourth and last square. The king readily agreed, before realizing that he had been deceived. By mid-chessboard, his castle was barely big enough to contain the grains, and just the first square of the other half would again double that. The story has been used by anyone from 13th century Islamic scholars to scientist/author Carl Sagan to social media videographers to explain the power of exponential sequences, where things begin small, very small...

Fermi Problems

It's a familiar peeve: The public doesn't understand science or its workings. Society would be stronger and safer if the citizenry could only judge the reliability of climate change studies, the benefits of vaccines, or even the significance of the Higgs boson. This plaint sounds both worthy and familiar, but to lament the impoverished state of science literacy is to flog an expired equine. It's easy to do, but neither novel nor helpful. Of course, that's not to say that we shouldn't try. The teaching and popularization of science are The Lord's work. But one can easily allow the perfect to become the enemy of the good. Rather than hope for a future in which everyone has a basic understanding of atomic theory or can evaluate the statistical significance of polls, I'm willing to aspire to a more conditional victory. I would appreciate a populace able to make order-of-magnitude estimates. This is a superbly useful skill, and one that can be acquired by young people with no more than a b...

Natural Selection

It's easy to think of natural selection as omnipotent. As Darwin said, "natural selection is daily and hourly scrutinizing...every variation, even the slightest; rejecting that which is bad, preserving and adding up all that is good." And the end result? Through time, a population becomes better and better adapted. Given enough time, wouldn't we expect natural selection to construct the ideal organism, optimally designed to meet the demands of its environment? If natural selection worked like an engineer—starting with a blank slate and an unlimited range of materials, designing a blueprint in advance to produce the best possible structure—then the result might indeed be perfection. But that's not a good analogy for how natural selection works. As Nobel laureate Francois Jacob suggested in 1977, the better metaphor is a tinkerer who "gives his materials unexpected functions to produce a new object. From an old bicycle wheel, he makes a roulette; from a broken chair the cabinet of a radio....

Embodied Thinking

Many have chosen the cosmic, appropriately in these heady times of gravity waves and Einstein anniversaries. The secrets of the universe. But how did Einstein arrive at his cosmic revelations? Through his body, imagining being hurled into space at cosmic speed. Not through the equations that proved his theories nor through the words that explain them. Imagining bodies moving in space. This is the very foundation of science, from the cosmic, bright stars and black holes and cold planets, to the tiny and tinier reverberating particles inside particles inside particles. The foundation of the arts, figures swirling or erect on a canvas, dancers leaping or motionless on a stage, musical notes ascending and descending, staccato or adagio. The foundation of sports and wars and games. And the foundation of us. We are bodies moving in space. You approach a circle of friends, the circle widens to embrace you. I smile or wince and you feel my joy or my pain, perhaps smiling or wincing with me. Ou...

Unruh Radiation

Many people have heard of Hawking radiation, which is a form of radiation emitted by a black hole. Less familiar is Unruh radiation, named after Bill Unruh who first described it. It also is emitted by black holes. Close to a black hole, the radiation is predominantly Unruh; further away, it is predominantly Hawking. Unruh radiation is observed by a detector when it is placed in a state of uniform acceleration, whereas if the same detector is at rest or in a state of uniform motion, no radiation is observed. The Unruh radiation in the case of uniform acceleration is like a black body with a temperature proportional to the acceleration. The relevance to black holes is that, close to a black hole, the geometry of a spherical black hole can be transformed so that it looks like that of a uniformly accelerated object. John Bell suggested that Unruh radiation might be observed in an electron storage ring. ...

The Genetic Book of the Dead

Natural Selection equips every living creature with the genes that enabled its ancestors—a literally unbroken line of them—to survive in their environments. To the extent that present environments resemble those of the ancestors, to that extent is a modern animal well equipped to survive and pass on the same genes. The 'adaptations' of an animal, its anatomical details, instincts and internal biochemistry, are a series of keys that exquisitely fit the locks that constituted its ancestral environments. Given a key, you can reconstruct the lock that it fits. Given an animal, you should be able to reconstruct the environments in which its ancestors survived. A knowledgeable zoologist, handed a previously unknown animal, can reconstruct some of the locks that its keys are equipped to open. Many of these are obvious. Webbed feet indicate an aquatic way of life. Camouflaged animals literally carry on their backs a picture of the environments in which their ancestors evaded predation. But mos...

The Copernican Principle

Nicolaus Copernicus taught us in the 16th century that we are nothing special, in the sense that the Earth on which we live is not at the center of the solar system. This realization, which embodies a principle of mediocrity on the astrophysical scale, has become known as The Copernican Principle. In the centuries that have passed since Copernicus's discovery, it seems that the Copernican principle has significantly gained strength, through a series of steps that have demonstrated that our place in the cosmos is of lesser and lesser importance. First, astronomer Harlow Shapley showed at the beginning of the 20th century that the solar system is not at the center of the Milky Way galaxy. It is in fact about two thirds of the way out. Second, recent estimates based on searches for extrasolar planets put the number of Earth-size planets in the Milky Way in the billions. A good fraction of those are even in that "Goldilocks" region (not too hot not too cold) around their host stars, that ...

Ocean Acidification

Ocean acidification, a stealthy side effect of rising anthropogenic CO2 emissions, is a recently discovered, little recognized global climate change threat that ought be more widely known. Unlike the warming effect on air temperatures that rising atmospheric CO2 levels cause—which scientists have understood theoretically since the late 1800s and began describing forcefully in the late 1970s—the alarm bell for ocean acidification was rung only in 2003, in a brief scientific paper. It introduced the term "ocean acidification" to describe how some of the rising CO2 levels are absorbed and dissolved into surface waters of the ocean. This has the benefit of slowing the pace of air temperature warming (thus far, oceans have absorbed at least a quarter of anthropogenic CO2 emissions) but the detriment of lowering the pH of the world's oceans. In chemistry notation, dissolving carbon dioxide in water yields carbonic acid (CO2 + H2O ↔ H2CO3), which quickly converts into bicarbonate (HCO3-) and ...

Paleoneurology

On a brisk May day, in 1967, Tilly Edinger crossed a peaceful, leafy Cambridge, Massachusetts street for the last time. Ironic, given that she survived challenge after challenge. In the 1920s, after becoming a paleontologist against her father's, and the profession's, wishes, Edinger and a few others began systematically measuring the fossilized heads of various animals and human ancestors. The idea was to understand the evolution of the cranial cavity and attempt to infer changes in brain anatomy, thus birthing paleoneurology. Then she lost everything, fleeing Frankfurt just after Kristallnacht. As Hitler wiped out most of her relatives, she painstakingly rebuilt her life in the US. Although a lifelong friend and correspondent of Einstein, she led a somewhat reclusive existence, and, as occurred with Rosalind Franklin, she was somewhat underestimated and unappreciated. On May 6th she left Harvard's Museum of Comparative Zoology and, having lost most of her hearing in her teenage years...

The Cancer Seed and Soil Hypothesis

One in 2 men and 1 in 3 women in the US will get cancer. Five decades after declaring war on the disease, we are still muddling our way rather blindly from the slash-poison-burn (surgery-chemo-radiation) strategies to newer approaches like targeted therapies, nanotechnology, and immunotherapies which benefit only a handful of patients. Among other reasons for the slow progress, a major flaw is the study of cancer cells in isolation, which de-links the seed from its soil. Stephen Paget was the first to propose in 1889 that "seeds" (cancer cells) preferentially grew in the hospitable "soil" (microenvironment) of select organs. The cross-talk between seed-soil hypothesized by Paget indeed proved to be the case whenever the question was examined (such as in the elegant studies of Hart and Fiddler in the 1980s). Yet, consistent research combining studies of the seed and soil were not pursued, largely because in the excitement generated by the molecular revolution and discovery of oncogenes,...

Negativity Bias

One of the most understated effects in all cognitive science is the psychology behind why negative events, emotions, and thoughts trump by a wide margin those that are positive. This bias was discovered and documented by the psychologists Paul Rozin and Edward Royzman in 2001, showing that across almost all domains of life, we seem almost preternaturally pessimistic: • Negative stimuli command more attention than positive stimuli. In rats, for example, negative tastes elicit stronger responses than positive tastes. And in taste aversion experiments a single exposure to a noxious food or drink can cause lasting avoidance of that item, but there is no corresponding parallel with good tasting food or drinks. • Pain feels worse than no pain feels good. That is, as the philosopher Arthur Schopenhauer put it, "we feel pain, but not painlessness." There are erogenous zones, Rozin and Royzman point out, but no corresponding torturogenous zones. • Picking out an angry face in a crowd is easier ...

Information Pathology

Our modern world of digitized bits moving with ever-increasing density and speed through a skein of channels resembling an electronic nervous system is built on information. The theory of information was borne full-blown from the head of Claude Shannon in a seminal paper published in 1948. Shannon provided the means—but not the meaning—for this remarkable feat of engineering. Now, as we are coming to realize with increasing urgency, we have to put the meaning back in the message. Information theory has given us big electronic pipes, data compression, and wonderful applications for distinguishing signal from noise. Internet traffic is ballooning into the realm of zettabytes—250 billion DVDs-worth of data—but the theory underlying these advances provides no way to get from information to knowledge. Awash in propaganda, conspiracy theories, and other signs of information sickness, we are giving way to the urge to exit from modernity itself. What is it about information that is making us s...

Effective Theory

People can disagree about many deep and fundamental questions, but we are all pretty confident that when we sit on a hard wooden chair it will support us, and that when we take a breath on the surface of the Earth we will take in the oxygen we need to survive. Yet, ultimately that chair is made of molecules, which are made of atoms composed of nuclei—protons and neutrons—with electrons orbiting them with probability functions in agreement with quantum mechanical calculations. Those electrons are on average very far from the nuclei, meaning from a perspective of matter, they are mostly empty space. And those protons and neutrons are made of quarks bound together by the dynamics of the strong force. No one knew about quarks until the second half of the 20th century. And despite the wisdom of the ancient Greeks, no one really knew about atoms either until at best a couple of hundred years ago. And of course air contains oxygen molecules and many others, too. Yet people had no trouble brea...

Polygenic Scores

Polygenic scores are beginning to deliver personal genomics from the front lines of the DNA revolution. They make it possible to predict genetic risk and resilience at the level of the individual rather than at the level of the family, which has far-reaching implications for science and society. Polygenic means many genes. Classical genetic studies over the past century have consistently supported Ronald Fisher's 1918 theory that the heritability of common disorders and complex traits is caused by many genes of small effect. What had not been realized until recently was just how many and how small these effects are. Systematic gene-hunting studies began a decade ago using hundreds of thousands of DNA differences throughout the genome, called genome-wide association (GWA). The early goal was to break the 1% barrier, that is, to achieve the power to detect DNA associations that account for less than 1% of the variance of common disorders and complex traits. Samples in the tens of thousan...

Affordances

Psychologist James J. Gibson introduced the term affordance way back in the seventies. The basic idea is that the perceptual systems of any organism are designed to "pick up" the information that is relevant to its survival and ignore the rest. The relevant information is about opportunities "afforded" by the furnishings of the world: holes afford hiding in, cups afford drinking out of, trees afford climbing (if you're a child or a monkey or a bear, but not a lion or a rabbit), and so forth. Affordances make a nicely abstract category of behavioral options that can be guided by something other than blind luck—in other words, by information extracted from the world. Affordances are "what the environment offers the animal for good or ill," according to Gibson, and "the information is in the light." (Gibson, like most psychologists and philosophers of perception, concentrated on vision.) While many researchers and theoreticians in the fledgling interdisciplinary field of cognitive scien...

Recursion

Recursion resides at the core of all intelligence. Recursion requires the ability to reference an algorithm or procedure, and keep the reference distinct from the contents. And this capacity to refer is a centerpiece of the way that organisms form models of the world around them and even of themselves. Recursion is a profoundly computational idea and lies at the heart of Godel's incompleteness theorem and the philosophical consequences that flow from that work. Turing's own work on computable numbers requires recursion at its center. It's an open question about how recursion is implemented biologically, but one could speculate that it has been discovered by evolution many times. ...

Possibility Space

Some problems are easy, but most problems are hard. They exceed humans' ability to grasp and reason about possible answers. That's not just true of complex scientific and political problems, like making complex economic decisions or building models to address climate change. It's also true of ordinary life. "Let's get dinner tonight." "Okay, but where?" Questions like these quickly descend into existential crisis without some structure. "Who am I, even?" One way that mathematicians think about complex problems is by means of the possibility space of their possible solutions. (It's also sometimes called a solution space, or probability space.) In mathematics, possibility spaces are used as a register or ledger of all the possible answers to a problem. For example, the possibility space for a toss of a coin is heads or tails. Of two coins: heads-heads, heads-tails, tails-heads, and tails-tails. That's a simple enough example, because any given subset of the possibility space can be measu...

Spontaneous Symmetry Breaking

Spontaneous symmetry breaking is widespread and fundamental in physics and science. The most famous occurrence is that it is the mechanism responsible for the importance of Higgs physics, the reason quarks and electrons are allowed to have mass, and for the vacuum of our universe not being nothing. The notion is widespread in condensed matter physics, and indeed was first understood there. But it is much broader, potentially leading to confusion between theories and solutions in many areas. The basic idea can be explained simply and generally. Suppose a theory is stated in terms of an equation, X times Y =16. For simplicity consider only positive integer values of X, Y as solutions. Then there are three solutions, X=1 and Y=16, X=2 and Y=8, and X=Y=4. What is important is that the theory (XY=16) is symmetric if we interchange X and Y, but some solutions are not. The most famous example is that the theory of the solar system has the Sun at the center and is spherically symmetric, but th...

Stigler's Law of Eponymy

Stigler's law of eponymy says that no scientific discovery is named for its original discoverer. Notable examples include the Pythagorean theorem, Occam's razor, Halley's comet, Avogadro's number, Coriolis force, Gresham's law, Venn diagrams, Hubble's law... Statistician Stephen Stigler coined this law in a 1980 festschrift honoring sociologist Robert K. Merton. It was Merton who had remarked that original discovers never seem to get credit. Stigler playfully appropriated the rule, ensuring that Stigler's law would be self-referential. The generalization is not limited to science. Elbridge Gerry did not invent gerrymandering, nor Karl Baedeker the travel guide. Historians of rock music trace the lineage of the Bo Diddley beat, which didn't originate with that bluesman. The globe is filled with place names honoring explorers who discovered places already well known to indigenous peoples (Hudson River, Hudson Bay; Columbia, District of Columbia and Columbus, Ohio; etc. Perhaps there are ex...

The Second Law of Thermodynamics

The Second Law of Thermodynamics states that in an isolated system (one that is not taking in energy), entropy never decreases. (The First Law is that energy is conserved; the Third, that a temperature of absolute zero is unreachable.) Closed systems inexorably become less structured, less organized, less able to accomplish interesting and useful outcomes, until they slide into an equilibrium of gray, tepid, homogeneous monotony and stay there. In its original formulation the Second Law referred to the process in which usable energy in the form of a difference in temperature between two bodies is dissipated as heat flows from the warmer to the cooler body. Once it was appreciated that heat is not an invisible fluid but the motion of molecules, a more general, statistical version of the Second Law took shape. Now order could be characterized in terms of the set of all microscopically distinct states of a system: Of all these states, the ones that we find useful make up a tiny sliver of ...

Neoteny

The axolotl is a peculiar amphibian: it never undergoes metamorphosis, retaining its gills and living in water through its entire life, a kind of tadpole with feet. Studying the axolotl in the late 19th century, the German zoologist Julius Kollmann coined the term "neoteny" to describe this process—the retention of youthful traits into adulthood. Neoteny has gone on to have a provocative history within biology. Evolutionary biologists throughout the twentieth century, including Stephen Jay Gould, discussed and debated neoteny as one of the mechanisms of evolution and one of the distinguishing features of Homo sapiens in particular. Compared to our fellow primates, we mature later, more slowly, and somewhat incompletely: we stay relatively hairless, with larger heads, flatter faces, bigger eyes. Human adults, that is, strongly resemble chimpanzee infants. (Intriguingly, our typical depiction of an even more highly evolved species than ourselves—namely, aliens—is one of enormous heads...

Naïve Realism

The comedian George Carlin once noted "that anyone driving slower than you is an idiot and anyone going faster than you is a maniac." The obscure scientific term explaining why we see most people other than ourselves as unintelligent or crazy is naïve realism. Its origins trace back to at least the 1880s when philosophers used the term to suggest we ought to take our perceptions of the world at face value. In its modern incarnation, it has taken on almost the opposite meaning, with psychologist Lee Ross using the term to indicate that although most people take their perceptions of the world at face value, this is a profound error that regularly causes virtually unresolvable conflicts between people. Imagine three drivers in Carlin's world—Larry, Moe, and Curly. Larry is driving 30 MPH, Moe is driving 50 MPH, and Curly is driving 70 MPH. Larry and Curly agree that Moe's driving was terrible, but are likely to come to blows over whether Moe is an idiot or a maniac. Meanwhile, Moe disagre...

Impossible

The concept of "impossible" underlies all fundamental theories of physics; yet its exact meaning is little known. The impossibility of cloning, or copying, certain sets of states is at the heart of quantum theory and of quantum information. The impossibility of exceeding the speed of light is a fundamental feature of the geometry of spacetime in relativity. The impossibility of constructing perpetual motion machines is the core idea of thermodynamics: No machine can exist that produces energy without consuming any; and the second law demands the impossibility of machines converting "heat" (such as energy stored in the sea at room temperature) completely into "work" (energy that is useful, in that it can be used, for instance, to power a mill). But what do we mean, exactly, by impossible? The concept of impossible in physics is deep and has beautiful implications; it sharpens the everyday meaning of the word "impossible," giving to that airy nothing a solid, firm, deep connotation, root...

Illusory Conjunction

The concept of an illusory conjunction is not sufficiently explored in studies of perception and memory, and it is rarely discussed in philosophy. Yet this concept is of considerable importance to our understanding of perceptual and cognitive function. For example, when we hear a musical tone, we attribute a pitch, a loudness, a timbre, and we hear the tone as coming from a particular spatial location; so each perceived tone can be described as a bundle of attribute values. It is generally assumed that this bundle reflects the characteristics and location of the sound that is emitted. However, when multiple sequences of tones arise simultaneously from different regions of space, these bundles of attribute values sometimes fragment and recombine incorrectly, so that illusory conjunctions result. This gives rise to several illusions of sound perception, such as the octave illusion and the scale illusion, in which the melodies we "hear" are quite different from those that are presented. T...

Matter

The concept of matter ought to be more widely known. You might wonder, did I misunderstand the question? Did I think it was asking, "What scientific term or concept is already widely known?" For if there is any scientific concept that is widely known, then it's the concept of matter, i.e. that stuff from which all things are made. But no, I didn't misread the question. While every intelligent person has heard of the concept of "matter," few people know the scientific meaning of the word. What we have here is an example of a concept that was first used in ordinary life, but that has come to be explicated in the development of science. So what does science tell us about matter? As you probably know, there's an age-old debate about whether things are ultimately made out of particles, or whether things are excitations or waves in some continuous medium. (In fact, the philosopher Immanuel Kant found this debate so tedious that he declared it irresolvable in principle.) But many of us were t...

Peircean Semiotics

The course followed by humans on the path to language was a progression through natural signs to human symbols. Signs and symbols are explained in reference to a theory of "semiotics," the study of signs, in the writings of Charles Sanders Peirce (1839-1914, usually known simply as C.S. Peirce). Peirce was perhaps the most brilliant American philosopher who ever lived. Bertrand Russell said of him, "Beyond doubt ... he was one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever." He contributed to mathematics, to science, to the study of language, and to philosophy. He is the founder of multiple fields of study, including semiotics, the study of signs, and pragmatism, the only uniquely American school of philosophy, further developed by William James and others. Peirce's theory of semiotics outlines a conceptual progression of signs from indexes, to icons, to human-created symbols. This progression moves to an increasing complexi...

The Noösphere

The idea of the "Noösphere," or "the sphere of mind," emerged early in the 20th century. It flourished for a while, then vanished. It deserves a second chance. The Noösphere belongs to a family of concepts describing planetary envelopes or domains that have shaped the earth's history: biosphere, hydrosphere, atmosphere, lithosphere, and so on. The idea of a distinct realm of mind evolved over several centuries. The 18th-century French naturalist, Buffon, wrote of a "realm of man" that was beginning to transform the earth's surface. Nineteenth-century environmental thinkers such as George Perkins Marsh tried to measure the extent of those transformations, and Alexander von Humboldt declared that our impact on the planet was already "incalculable." The word "Noösphere" emerged in Paris, in 1924, from conversations between the Russian geologist, Vladimir Vernadsky, and two French scholars, the paleontologist and priest, Teilhard de Chardin, and the mathematician, Édouard Le Roy. In a lect...

The Ideal Free Distribution

The gist of the "ideal free distribution" is that individuals in the best of all possible worlds should distribute themselves in the best of all possible ways. They should sort themselves out across space and time so as to avoid predators, find prey, get mates, and leave as many descendants as they can behind. Where information is imperfect, the best spots will be missed; and where mobility is blocked, distributions will be "despotic." But where information is unlimited and mobility is unrestrained, distributions will be "ideal" and "free." The idea is intuitively obvious, and it has predictive power. It works for aphids. It works for sticklebacks. And it works for us. Over most of the long stretch of the human past, our distributions were more or less ideal-free. We usually moved around with our prey, following the plants we collected and the animals we tracked. Some foragers, even now, are more footloose than others: On the Kalahari, hunters with access to waterholes, or n!oresi, mak...

Confirmation Bias

The great promise of the Internet was that more information would automatically yield better decisions. The great disappointment is that more information actually yields more possibilities to confirm what you already believed anyway. ...

The Trolley Problem

The history of science is littered with "thought experiments," a term dreamed up by Albert Einstein ("gedankenexperiment") for an imagined scenario able to sharply articulate the crux of some intellectual puzzle, and in so doing excite some deep thinking on the way to a solution or related discovery. Among the most famous are Einstein's tale of chasing a light beam that led him to a theory of special relativity and Erwin Schrödinger's story of the poor cat, stuck in a fiendishly designed quantum mechanical box, forever half-alive and half-dead, that highlighted the complex interactions between wave mechanics and measurement. "The Trolley Problem" is another thought experiment, one that arose in moral philosophy. There are many versions, but here is one: A trolley is rolling down the tracks and reaches a branchpoint. To the left, one person is trapped on the tracks, and to the right, five people. You can throw a switch that diverts the trolley from the track with the five to the track w...

Comparative Advantage

The intuitively clear effects of a tariff—a tax on goods or services entering a country—are that it helps domestic producers of the good or service and harms foreign producers. An American tax on Chinese tires, say, transparently helps American tire producers because the prices of the tires of their foreign competitors will be higher, allowing American producers to compete more easily. Those are the intuitively clear effects. These effects—advantages for domestic firms, disadvantages for foreign firms—are useful for politicians to emphasize when they are contemplating tariffs and other forms of protectionism because they appeal to nationalistic, competitive intuitions. However, not all ideas surround international trade are so intuitive. Consider these remarks by economist Paul Krugman: "The idea of comparative advantage—with its implication that trade between two nations normally raises the real incomes of both—is, like evolution via natural selection, a concept that seems simple ...

Simplistic Disease Progression

The leading killer diseases—heart and cancer—don't follow old dogma. The two leading causes of death are heart attacks and cancer. For much too long we've had the wrong concept about the natural history of these conditions. There are common threads for these two diseases: People generally don't die of cholesterol buildup in their arteries (atherosclerosis) unless they have a heart attack or stroke; similarly, cancer rarely causes death unless it metastasizes. For decades, it was believed that cholesterol build up inside an artery supplying the heart muscle followed a slow, progressive development. As the plaque grew bigger and bigger, as the theory goes, it eventually would clog up the artery and cause interruption of blood supply—a heart attack. That turned out not to be true at all, since it's the minor cholesterol narrowings that are, by far, the most common precursors to a heart attack. The heart attack results from a blood clot as the body tries to seal a sudden crack in the wall ...

The Holographic Principle

The most famous case study in science, prior to Freud, was published in 1728 in the Philosophical Transactions of the Royal Society by the English surgeon William Cheselden, who attended Newton in his final illness. It bore a snappy title: "An Account of Some Observations Made by a Young Gentleman, Who Was Born Blind, or Lost His Sight so Early, That He Had no Remembrance of Ever Having Seen, and Was Couch'd between 13 and 14 Years of Age." The poor boy "was couch'd"—his cataracts removed—without anesthesia. Cheselden reported what he then saw: When he first saw, he was so far from making any Judgment about Distances, that he thought all Objects whatever touch'd his Eyes, (as he express'd it) as what he felt, did his Skin . . . We thought he soon knew what Pictures represented, which were shew'd to him, but we found afterwards we were mistaken; for about two Months after he was couch'd, he discovered at once, they represented solid Bodies. The boy saw, at first, patterns and colors p...

"The Big Bang"

The name "Big Bang" has been misleading scientists, philosophers, and the general public since Sir Fred Hoyle said it on radio in 1949. It conjures up the image of a giant firecracker, an ordinary explosion happening at a place and a time, a collection of material suddenly beginning to expand into the surrounding empty space. But this is so exactly opposite to what astronomers have observed that it is shocking we still use the name, and it is not the least bit surprising that some people object to it. Einstein didn't like it at first but became convinced. Hoyle never liked it at all. People might like it better if they knew what it meant. What astronomers actually have observed is that distant galaxies all appear to be receding from us, with a speed roughly proportional to their distance. We've known this since 1929, when Edwin Hubble drew his famous plot. From this we conclude a few simple things. First, we can get the approximate age of the universe by dividing the distance by the sp...

Need For Closure

The poet John Keats coined the term negative capability to refer to the ability to remain content with half-knowledge "without any irritable reaching after fact and reason." The opposite of negative capability is known by psychologists as the need for closure (NFC). NFC refers to an aversion toward ambiguity and uncertainty, and the desire for a firm answer to a question. When NFC becomes overwhelming, any answer, even a wrong one, is preferable to remaining in a state of confusion and doubt. If we could represent the knowledge in any given brain as dry land, and ignorance as water, then even Einstein's brain would contain just a few tiny islands scattered around in a vast ocean of ignorance. Yet most of us find it hard to admit how little we really know. How often, in the course of our everyday conversations, do we make assertions for which we have no evidence, or cite statistics that are really nothing but guesses? Behind all these apparently innocuous confabulations lies NFC. Th...

Sex

The poet Philip Larkin famously proclaimed that sex began in 1963. He was inaccurate by 800 million years. Moreover, what began in the 1960s was instead a campaign to oust sex—in particular sex differences—in favor of gender. Why? Because biological differences were thought to spell genetic determinism, immutability, anti-feminism and, most egregiously, women's oppression. Gender, however, was the realm of societal forces; "male" and "female" were social constructs, the stuff of political struggle; so gender was safe sex. The campaign triumphed. Sex now struggles to be heard over a clamor of misconceptions, fabrications and denunciations. And gender is ubiquitous, dominating thinking far beyond popular culture and spreading even to science—such that a respected neuroscience journal recently felt the need to devote an entire issue to urging that sex should be treated as a biological variable. And, most profoundly, gender has distorted social policy. This is because the campaign has unde...

The Navier-Stokes Equations

The question puts us in danger of resembling the man who only looks for his dropped watch under the light of a street lamp: the scientific concept that has the widest impact in our lives may not necessarily be the simplest. The Navier-Stokes equations date from 1822 and apply Newton's Second Law of Motion to viscous fluids. The range of applications is vast—in weather prediction, aircraft and car design, pollution and flood control, hydro-electric architecture, in the study of climate change, blood flow, ocean currents, tides, turbulence, shock waves and the representation of water in video games or animations. The name of Claude-Louis Navier is to be found inscribed on the Eiffel Tower, whereas the Irishman, George Stokes, once president of the Royal Society, is not well known outside of maths and physics. Among many other achievements, Stokes laid the foundations of spectroscopy. It needs a John Milton of mathematics to come down among us and metamorphose the equations into lyrical E...

Cognitive Ethology

The term "cognitive ethology" was coined and used by Donald Griffin in the late 1970s- early 1980s to describe a field that he was among the first to champion—the study of versatile thinking by nonhumans and, importantly, how the data obtained could be used to examine the evolution and origins of human cognition. His further emphasis on the study of animal consciousness, however, caused many of his colleagues to shun all his ideas, proverbially "throwing out the baby with the bath water." Griffin's term, "cognitive ethology," nevertheless deserves a closer look and a renaissance in influence. The case is strengthened by an historical examination of the subject. In the 1970s and 1980s, researchers studying nonhuman abilities were slowly moving away from the two ideologies that had dominated psychology and much of behavioral biology for decades—respectively, behaviorism and fixed-action patterns—but progress was slow. Proponents of behaviorism may have argued that little difference exist...

Chronobiology

The time-is-money ethos of the Industrial Age and wage labor, combined with the generic quality of computerized time-keeping and digital calendars has all but disconnected us from the temporal rhythms on which biological life has oriented itself for millennia. Like all organisms, the human body has evolved to depend on the cyclical ebbs and flows of light, weather, and even the gravitational pull of the moon in order to function effectively. But our culture and its technologies are increasingly leading us to behave as if we can defy these cycles—or simply ignore them completely. We fly ten time zones in as many hours, drink coffee and take drugs to wake ourselves, pop sedatives to sleep, and then take SSRI's to counter the depression that results. We schedule our work and productivity oblivious to the way the lunar cycle influences our moods and alertness, as well as those of our students, customers, and workforces. Chronobiology is the science of the biological clocks, circadian rhyth...

Power Law

The way predictions are made is changing. Data scientists are competing with traditional statisticians, and "big data" analysis is competing with the study of "statistic samples." This change mirrors a wider paradigm shift in the conception of society and in what rules its structural dynamics. In order to understand this change, one needs to know the "power law." If facts happen randomly, in a two-axis world, it is very much possible that they will distribute as in a Gaussian curve, in the shape of a bell, with a majority of happenings concentrating around the average. But if facts are interlinked and if they co-evolve in such a way that a change in one quantity results in a proportional change in the other quantity, it is more probable that they will distribute as in a power law graph, in a ski jump shape, in which the average is not important and polarization is unavoidable. The distributions of a large set of phenomena observed in physics, biology, astronomy follow a power law, but...

Equipoise

There is an old word in our language, equipoise, which has been around since at least the 16th century—when it meant something like "an equal distribution of weight." With respect to science, it means, roughly, standing at the foot of a valley and not knowing which way is best to proceed to get up high—poised between alternative theories and ideas about which, given current information, one is neutral. Use of the word peaked around 1840, and declined roughly five-fold since then, according to Google Ngram, though it appears to be enjoying an incipient resurgence in the last decade. But attention to equipoise ought to be greater. The concept found a new application in the 1980s, when ethicists were searching for deep justifications for the conduct of randomized clinical trials in medicine. A trial was only justified, they rightly argued, when the doctors and researchers doing the trial (and the medical knowledge they were relying on) saw the new drug or its alternative (a placebo, perh...

Iatrotropic Stimulus

This concept comes from epidemiology, the field of medicine comprising methods used to find the causes of health outcomes and diseases in populations. The meaning and relevance of this term require some historical background. When I was a medical student almost fifty years ago, I learned this concept from Dr. Alvan Feinstein, a professor of both medicine and epidemiology at Yale. He taught a course in clinical diagnosis that would prepare us for seeing patients in the hospital. A strict and exacting teacher, he demanded that we learn to take a detailed and carefully crafted patient history, combined with a meticulous physical examination that were both crucial, he believed, to the art and science of medicine. Dr. Feinstein, as a cardiologist, had helped delineate the criteria that defined rheumatic heart disease. The critical role that rheumatic fever—caused by Streptoccocal infection—played in its pathogenesis could then be firmly established, so that early treatment of this infecti...

Digital Representation

Three people stand in front of a portrait in a museum, each making a copy of it: an art student producing a replica in paint; a professional photographer taking a picture of it with an old film camera; and a tourist snapping a photo with a phone. Which one is not like the others? The art student is devoting much more time to the task, but there's a sense in which the tourist with the phone is the odd one out. Paint on canvas, like an exposed piece of film, is a purely physical representation: a chemical bloom on a receptive medium. There is no representation distinct from this physical embodiment. In contrast, the cell phone camera's representation of the picture is fundamentally numerical. To a first approximation, the phone's camera divides its field of view into a grid of tiny cells, and stores a set of numbers to record the intensity of the colors in each of the cells that it sees. These numbers are the representation; they are what get transmitted (in a compressed form) when the ...

Alloparenting

To alloparent is to provide care for offspring that are not your own. It is a behavior that is unimaginable for most species (few of which even care for their own offspring), rare even among relatively nurturant classes of animals like birds and mammals, and central to the existence of humankind. The vigor and promiscuity with which humans in every culture around the world alloparent stands in stark contrast to widespread misconceptions about who we are and how we should raise our children. Humans' survival as a species over the last 200,000 years has depended on our motivation and ability to care for one another's children. Our babies are born as helpless and needy as it is possible for a living creature to be. The actress Angelina Jolie was once derided for describing her newborn as a "blob," but she wasn't far off. Human infants arrive into the world unable to provide the smallest semblance of care for themselves. Worse, over a decade will pass before a human child becomes self-suff...

The Anthropocene

To understand earthquakes in Oklahoma, the Earth's sixth mass extinction, or the rapid melting of the Greenland Ice Sheet, we need the Anthropocene—an epoch that acknowledges humans as a global, geologic force. The Holocene, a cozier geologic epoch that began 11,700 years ago with climatic warming (giving us conditions that, among other things, led to farming), doesn't cut it anymore. The Holocene is outdated because it cannot explain the recent changes to the planet: the now 400 parts per million of carbon dioxide in the atmosphere from burning fossil fuels, the radioactive elements present in the Earth's strata from detonating nuclear weapons, or that one in five species in large ecosystems is considered invasive. Humans caused nearly all of the 907 earthquakes in Oklahoma in 2015 as a result of the extraction process for oil and gas, part of which involves injecting saltwater, a byproduct, into rock layers. The Anthropocene is defined by a combination of large-scale human impacts an...

Haldane's Rule of the Right Size

Toss a mouse from a building. It will land, shake itself off and scamper away. But if similarly dropped, "... a rat is killed, a man is broken, a horse splashes." So wrote J.B.S. Haldane in his 1926 essay "On Being the Right Size." Size matters, but not in the way a city-stomping Godzilla or King Kong might hope. Every organism has an optimum size and a change in size inevitably leads to a change in form. Tiny lizards dance weightlessly up walls, but grow one to Godzilla size, and the poor creature would promptly collapse into a mush of fractured bones and crushed organs. This principle is not just a matter of extremes: A hummingbird scaled to the size of a blue jay would be left hopelessly earthbound, fluttering its wings in the dust. If gravity is the enemy of the large, surface tension is the terror of the small. Flies laugh at gravity, but dread water. As Haldane notes, "An insect going for a drink is in as great danger as a man leaning out over a precipice in search of food." No won...

Case-Based Reasoning

We do case-based reasoning all the time, without thinking that that is what we are doing. Case-based reasoning is essential to personal growth and learning. While we hear people proclaim that mathematics teaches one to think, or knowing logic will help one reason more carefully, humans do a different kind of reasoning quite naturally. When we go to a restaurant, we think about what we ordered the last time we were there and whether we want to order the same thing again. When we go out on a date, we think about how that person reminds us of someone we went out with before, and we think about how that turned out. When we read a book we are reminded of other books with similar themes or similar situations and we tend to predict outcomes on that basis. When we hear someone tell us a story about their own lives, we are immediately reminded of something similar that has happened to us. Reminding, based on the examination of a internal library of cases, is what enables learning and is the bas...

Population Thinking

What were Darwin's most significant contributions? Ernst Mayr answered: (1) producing massive evidence of evolution, (2) explaining it in terms of natural selection, and (3) thinking about species as populations. "Population thinking"? Philosophers are still debating what this means. For scientists, however, to think of living things in terms of populations rather than types having each its own essence is a clear and radical departure both from earlier scholarly traditions and from folk biology. Species evolve, early features may disappear, novel features may appear. From a populationist point of view, a species is a population of organisms that share features not because of a common "nature" but because they are related by descent. A species so understood is a temporally continuous, spatially scattered entity that changes over time. Population thinking readily extends beyond biology to the study of cultural evolution (as argued by Peter Richerson, Robert Boyd, and Peter Godfrey-Smith)...

Number Sense

When I graduated with a bachelors degree in mathematics from one of the most prestigious university mathematics programs in the world (Kings College London) in 1968, I had acquired a set of skills that guaranteed full employment, wherever I chose to go, for the then-foreseeable future—a state of affairs that had been in existence ever since modern mathematics began some three thousand years earlier. By the turn of the new Millennium, however, just over thirty years later, those skills were essentially worthless, having been very effectively outsourced to machines that did it faster and more reliably, and were made widely available with the onset of first desktop- and then cloud-computing. In a single lifetime, then, I experienced a dramatic change in the nature of mathematics and how it played a role in society. The shift began with the introduction of the digital arithmetic calculator in the 1960s, which rendered obsolete the need for humans to master the ancient art of mental arithme...

Polythetic Entitation

When is a wine glass not a wine glass? This question fascinated the archaeological theorist David Clarke in the late 1960s, but his elegant solution, critical for a correct conceptualization of artefacts and their evolution over time, is shamefully ignored. Understanding polythetic entitation opens the door to a richer view of the built world, from doors to computers, cars to chairs, torches to toothbrushes. It is a basic analytical tool for understanding absolutely anything that people make. It indicates limits to the idea of the meme, and signals that it may be reasonable to consider the intentional patterning of matter by Homo sapiens as a new, separate kind of ordering in the universe. Celebrating the end of our archaeological excavation season, someone tops up my glass with wine . . . except it is not a glass. That is, it is not made of glass; it is a clear plastic disposable object, with a stem. Nevertheless, when I put it down on a table to get some food and then cannot find it,...

Evolve

When scientific concepts become metaphors, nuances of meaning often get lost. Some such errors are benign. In the vernacular, "quantum leap" has come to mean tremendous change. This misrepresents the physics, but usually without serious implications. There is no philosophy embedded in the metaphor that lends its misuse a particular power. Yet errors in translation are not always so neutral. As a popular metaphor, the concept "evolve" gets conflated with progress. Evolved means better, as if natural law normally dictates constant improvement over time. In translating progress from species evolution to the metaphor of evolve, the significance of dynamic relationship to a specific environment gets lost. Through natural selection, species become more equipped to survive in their distinct environment. In a different environment, they may find themselves vulnerable. Divorced from context, their measure of progress breaks down. The popular metaphor of evolve misses this crucial point. Evolve ...

Premature Optimization

Why do the successful often fail to repeat their success? Because success is often the source of failure. Success is a form of optimization—a state of optimal profits, or optimal fitness, or optimal mastery. In this state you can't do any better than you are. In biology, a highly evolved organism might reach a state of supreme adaptation to its environment and competitors to reach reproductive success. A camel has undergone millions of revisions in its design to perfect its compatibility with an arid climate. Or in business, a company may have spent many decades perfecting a device until it was the number one bestselling brand. Say it manufactured and designed a manual typewriter that was difficult to improve. Successful individuals, too, discover a skill they are uniquely fit to master—a punk rock star who sings in an inimitable way. Scientists use a diagram of a mountainous landscape to illustrate this principle. The contours of the undulating landscape indicate adaptive success of a...

Motivated Reasoning

Why, in an age in which we have the world's information easily accessible at our fingertips, is there still so much widespread disagreement between people about basic facts? Why is it so hard to change people's minds about truth even in the face of overwhelming evidence? Perhaps some of these inaccurate beliefs are the result of an increase in the intentional spreading of false information, a problem exacerbated by the efficiency of the internet. But false information has been spread pretty much since we've had the ability to spread information. More importantly, the same technologies that allow for the efficient spreading of false information also provide us with the ability to fact-check our information more efficiently. For most questions we can find a reliable, authoritative answer easier than anyone has ever been able to in all of human history. In short, we have more access to truth than ever. So why do false beliefs persist? Social psychologists have offered a compelling ans...

Quines

Within the infinite space of computer programs is a special subset of code: programs that, when executed, output that program itself. In other words, these are a kind of self-replicating program; when you run them, they yield themselves. These short programs are often referred to as quines, after the philosopher Willard Van Orman Quine, based on the term from Douglas Hofstadter's Gödel, Escher, Bach: an Eternal Golden Braid. Upon first hearing about quines, they often seem magical. And doubly so if you have ever done any coding, because without knowing the trick for how to create these, they might seem devilishly difficult to construct. They are often elegant little things, and there are now examples of quines in a huge number of computer languages. They can range from short and sweet ones to ones that are far more inscrutable to the untrained eye. But why are they important? Quines are a distillation of numerous ideas from computer science, linguistics, and much more. On a simple leve...

Actionable Predictions

You might be forgiven for thinking that this is so blindingly obvious that it is hardly worth stating, let alone arguing, that it should become a popular meme. After all, "pre-" means "before," so surely you should be able to take action in the wake of a prediction to change your future—like buying an umbrella when a deluge is forecast, for example. Weather forecasting is indeed a good example of an actionable prediction, a beautiful marriage of real-time data from satellites and other sensors with modeling. But when you shift your gaze away from the physical sciences towards medicine, these predictions are harder to discern. We are a long way from doctors being able to make routine and reliable actionable predictions about individual patients—which treatments will help them the most, which drugs will cause them the fewest side effects, and so on. The answers to many simple questions remain frustratingly elusive. Should I take an antibiotic for that sore throat? Will immunotherapy work...

DNA

You might feel that "DNA" is already one of the most widely known scientific terms—with 392 million Google hits and Ngram score rising swiftly since 1946 to surpass terms like bread, pen, bomb, surgery and oxygen. DNA even beats seemingly more general terms like genetics or inheritance. This super-geeky acronym for deoxyribonucleic acid (by the way, not an acid in nature, but a salt) has inspired vast numbers of clichés like "corporate DNA" and cultural tropes like crime scene DNA. It is vital for all life on earth, responsible for the presence of oxygen in our atmosphere, is present in every tissue of every one of our bodies. Nevertheless, knowing even a tiny bit (which could save your life) about your DNA in your own body has probably lagged behind your literacy of sports, fictional characters, and the doings of celebrities. The news is that you can now read all of your genes in detail for $499 and nearly your complete DNA genome for $999. The nines even make it sound like a consumer...

Common Sense

You're much more likely to hear "common sense" invoked as a concept at a cocktail party than at a scientific discussion. In fact, common sense should be invoked more often in scientific discussions, where it is sometimes deficient and scorned. Scientists may string out a detailed argument that reaches an implausible conclusion contradicting common sense. But many other scientists nevertheless accept the implausible conclusion, because they get caught up in the details of the argument. I was first exposed to this fallacy when my high school teacher of plane geometry, Mr. Bridgess, gave us students a test consisting of a 49-step proof on which we had to comment. The proof purported to demonstrate that all triangles are isosceles, i.e. have two equal sides. Of course that conclusion is wrong: most triangles have unequal sides, and only a tiny fraction has two equal sides. Yet there it was, a 49-step proof, couched in grammatically correct language of geometry, each step apparently impecca...

Bayes's Theorem

You're worried that your friend is mad at you. You threw a dinner party and didn't invite them; it's just the kind of thing they'd be annoyed about. But you're not really sure. So you send them a text: "Want to hang out tonight?" Twenty minutes later you receive a reply: "Can't, busy." How are we to interpret this new information? Part of the answer comes down to human psychology, of course. But part of it is a bedrock principle of statistical reasoning, known as Bayes's Theorem. We turn to Bayes's Theorem whenever we're uncertain about the truth of some proposition, and new information comes to light that affects the probability of that proposition being true. The proposition could be our friend's feelings, or the outcome of the World Cup, or a presidential election, or a particular theory about what happened in the early universe. In other words: we use Bayes's Theorem literally all the time. We may or may not use it correctly, but it's everywhere. The theorem itself isn't so hard: t...