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Fernanda Pirie is Professor of the Anthropology of Law at the University of Oxford. She is the author of  The Anthropology of Law and has conducted fieldwork in the mountains of Ladakh and the grasslands of eastern Tibet. She earned a DPhil in Social Anthropology from Oxford in 2002, an MSc in Social Anthropology at University College London in 1998, and a BA in French and Philosophy from Oxford in 1986. She spent almost a decade practicing as a barrister at the London bar. Her most recent book is  The Rule of Laws: A 4,000-Year Quest to Order the World.

Skeptic: Why do we need laws? Can’t we all just get along?

Fernanda Pirie: That assumes we need laws to resolve our disputes. The fact is, there are plenty of societies that do perfectly well without formal laws, and that’s one of the questions I explore in my work: Who makes the law, and why? Not all sophisticated societies have created formal laws. For instance, the ancient Egyptians managed quite well without them. The Maya and the Aztec, as far as we can tell, had no formal laws. Plenty of much smaller communities and groups also functioned perfectly well without them. So, using law to address disputes is just one particular social approach. I don’t think it’s a matter of simply getting along; I do believe it’s inevitable that people will come into conflict, but there are many ways to resolve it. Law is just one of those methods.

It’s inevitable that people will come into conflict, but there are many ways to resolve it. Law is just one of those methods.

Skeptic: Let’s talk about power and law. Are laws written and then an authority is needed to enforce them, which creates hierarchy in society? Or does hierarchy develop for some other reason, and then law follows to deal with that particular structure?

FP: I wouldn’t say there’s always a single direction of development. In ancient India, for example, a hierarchy gradually developed over several thousand years during the first millennium BCE, with priests—eventually the Brahmins—and the king at the top. This evolved into the caste system we know today. The laws came later in that process. Legal texts, written by the Brahmins, outlined rules that everyone—including kings—had to follow.

Skeptic: So, the idea of writing laws down or literally chiseling them in stone is to create something tangible to refer to.. Not just, “Hey, don’t you remember, I said six months ago you shouldn’t do that?” Instead, it’s formalized, and everyone has a copy. We all know what it is, so you can hold people morally accountable for their actions.

FP: Exactly. That distinction makes a big difference. Every society has customs and norms; they often have elders or other sources of authority, who serve as experts in maintaining their traditions. But when it’s just a matter of, “This is what we’ve always done—don’t you remember?” some people can conveniently forget. Once something is written down, though, it gains authority. You can refer to the exact words, which opens up different possibilities for exercising power. “Look, these are the laws—everyone must know and follow them.” But it equally creates opportunities for holding people accountable.

Skeptic: So it’s a matter of “If you break the law, then these are the consequences.” It’s almost like a logic problem—if P, then Q. There’s an internal logic to it, a causal reasoning where B follows A, so we assume A causes B. Is something like that going on, cognitively?

Once something is written down, it gains authority. You can refer to the exact words, which opens up different possibilities for exercising power.

FP: Well, that cause-and-effect form is a feature of many legal systems, but not all of them. It’s very prominent in the Mesopotamian tradition, which influenced both Jewish law and Islamic law, and eventually Roman law—the legal systems that dominate the world today. It’s associated with the specification of rights—if someone does this, they are entitled to that kind of compensation, or this must follow from that. But the laws that developed in China and India were quite different. The Chinese had a more top-down, punitive system, focused on discipline and punishment. It was still an “if-then” system, but more about, “If you do this wrong, you shall be punished.” It was very centralized and controlling. In Hindu India, the laws were more about individual duty: this is what you ought to do to be a good Hindu. If you’re a king, you should resolve disputes in a particular way. The distinctions between these systems aren’t always sharp, but the casuistic form is indeed a particular feature of certain legal traditions.

Laws have never simply been rules. They’ve created intricate maps for civilization. Far from being purely concrete or mundane, laws have historically presented a social vision, promised justice, invoked a moral order ordained by God (or the Gods), or enshrined the principles of democracy and human rights. And while laws have often been instruments of power, they’ve just as often been the means of resisting it. Yet, the rule of law is neither universal nor inevitable. Some rulers have avoided submitting themselves to the constraints of law—Chinese emperors did so for 2,000 years. The rule of law has a long history, and we need to understand that history to appreciate what law is, what it does, and how it can rule our world for better or worse.

The rule of law is neither universal nor inevitable. Some rulers have avoided submitting themselves to the constraints of law.

Skeptic: In some ways it seems like we are seeking what the economist Thomas Sowell calls cosmic justice, where in the end everything is settled and everyone gets their just desserts. One purpose of the Christian afterlife is that all old scores are settled. God will judge everything and do so correctly. So, even if you think you got away with something, in the long run you didn’t. There’s an eye in the sky that sees all, and that adds an element of divine order to legal systems.

FP: Absolutely, and that characterizes many of the major legal systems, especially those associated with religion. Take the Hindu legal system—it’s deeply tied to a sense of cosmological order. Everyone must follow their Dharma, and the Brahmins set up the rules to help people follow their Dharma, so they can achieve a better rebirth. Similarly, Islamic Sharia law, which has had a poor reputation in recent times, is seen as following God’s path for the world, guiding people on how they should behave in accordance with a divine plan. Even the Chinese, who historically had a more top-down and punitive system, claimed that their emperors held the Mandate of Heaven—that’s why people had to obey them and their laws. They were at the top of the pyramid because of such divine authority.

Of course, there have also been laws that are much more pragmatic—rules that merchants follow to maintain their networks, or village regulations. Not all law is tied to a cosmic vision, but many of the most impressive and long-lasting legal systems have been.

Islamic Sharia law is seen as following God’s path for the world. Even the Chinese, who historically had a more top-down and punitive system, claimed that their emperors held the Mandate of Heaven.

Skeptic: The Arab–Israeli conflict can be seen as two people holding a deed to the same piece of land, each claiming, “The title company that guarantees my ownership is God and His Holy Book.” Unfortunately, God has written more than one Holy Book, leading both sides to claim divine ownership, with no cosmic court to settle the dispute.

FP: That’s been the case throughout history—overlapping legal and political jurisdictions. Many people today are worried about whether the nation-state, as we know it, is breaking down, especially with the rise of supranational laws and transnational legal systems. But it’s always been like this—there have always been overlaps between religious laws, political systems, and social norms. The Middle East is a perfect example, with different religious communities living side by side. It hasn’t always been easy, but over time, people have developed ways of coexisting. The current political battles in the Middle East are part of this ongoing tension.

Skeptic: In your writing, you offer this great example from the Code of Hammurabi, 1755–1750 BC. It is the longest, best-organized, best-preserved legal text from the ancient Near East, written in the Old Akkadian dialect of Babylonian, and inscribed on a stone stele discovered in 1901.

“These are the judicial decisions that Hammurabi, the King, has established to bring about truth and a just order in his land.” That’s the text you quoted. “Let any wronged man who has a lawsuit”—interesting how the word ‘lawsuit’ is still in use today—”come before my image as King of Justice and have what is written on my stele read to him so that he may understand my precious commands, and let my stele demonstrate his position so that he may understand his case and calm his heart. I am Hammurabi, King of Justice, to whom Shamash has granted the truth.”

Many people today are worried about whether the nation-state, as we know it, is breaking down.

Then you provide this specific example: “If a man cuts down a tree in another man’s date orchard without permission, he shall pay 30 shekels of silver. If a man has given a field to a gardener to plant as a date orchard, when the gardener has planted it, he shall cultivate it for four years, and in the fifth year, the owner and gardener shall divide the yield equally, with the owner choosing first.”

This sounds like a modern business contract, or today’s U.S. Uniform Commercial Code.

FP: Indeed, it’s about ensuring fairness among the farmers, who were the backbone of Babylon’s wealth at the time. I also find it fascinating that there are laws dealing with compensation if doctors kill or injure their patients. We often think of medical negligence as a modern issue, but it’s been around for 4,000 years.

Skeptic: But how did they determine the value of, say, a stray cow or cutting down the wrong tree? How did they arrive at the figure of 30 shekels?

FP: That’s a really interesting question. These laws were meant to last, and even in a relatively stable society, the value of money would have changed over time. People have studied this and asked how anyone could follow these laws for the hundreds of years that the stele stood and people referred to it. My view is that these laws were more exemplary—they probably reflected actual cases, decisions that judges were making at the time.

Laws have never simply been rules; they have created intricate maps for civilization, presented a social vision, promised justice, invoked a moral order, and enshrined principles of democracy and human rights.

Although Hammurabi wrote down his rules, he didn’t expect people to apply them exactly as written, as we do with modern legal codes. Instead, they gave a sense of the kind of compensation that would be appropriate for different wrongs or crimes—guidelines, not hard rules. Hammurabi likely collected decisions from various judicial systems and grafted them into a set of general laws, but they still retain the flavor of individual judgments.

Skeptic: Is there a sense of “an eye for an eye, a tooth for a tooth”—where the punishment fits the crime, more or less?

The Code of Hammurabi inscribed on a basalt slab on display at the Louvre, Paris. (Photo by Mbzt via Wikimedia)

FP: Absolutely. Hammurabi was trying to ensure that justice was done by laying out rules for appropriate responses to specific wrongs, ensuring fairness in compensation. But it’s crucial to understand that the famous phrase, “an eye for an eye, a tooth for a tooth,” which appears first in Hammurabi’s code and later in the laws of the Book of Exodus, wasn’t about enforcing revenge. Even though there’s a thousand-year gap between Hammurabi and the Bible, scholars believe this rule was about limiting revenge, not encouraging it. It meant that if someone sought revenge, it had to be proportional—an eye for an eye—but no more.

In other words, they wanted to prevent cycles of violence that arise from feuds. In a feuding society, someone steals a sheep, then someone retaliates by stealing a cow, and then someone tries to take an entire herd of sheep. The feud keeps getting bigger and bigger. So, the “eye for an eye” rule was a pragmatic approach in a society where feuding was common. It was meant to keep things under control.

Skeptic: From the ruler’s perspective, a feud is a net loss, regardless of who’s right or wrong.

FP: Feuding is a very common way of resolving disputes, especially among nomadic people. The idea, which makes a lot of sense, is that if you’re a nomadic pastoralist, your wealth is mobile—it’s your animals that have feet, which can be moved around. That also makes it easy to steal. If you’re a farmer, your wealth is tied to your land, so someone can’t run off with it. Since nomads are particularly vulnerable to theft, having a feuding system acts as a defense mechanism. It’s like saying, “If you steal my sheep, I’ll come and steal your cow.” You still see this in parts of the world, such as eastern Tibet, where I’ve done fieldwork. So, yes, kings and centralized rulers want to stop feuds because they represent a net loss. They want to put a lid on things and so establish a more centralized system of justice. This is exactly what Hammurabi was trying to do, and you see similar efforts in early Anglo- Saxon England, and all over the world.

Another interesting point is that every society has something to say about homicide. It’s so important that they have to lay out a response. However, I don’t think we should assume these laws were meant to stop people from killing each other. The fact is, we don’t refrain from murder because the law tells us not to. We don’t kill because we believe it’s wrong—except in the rare cases where morality has somehow become twisted and self-help justice occurs and people take the law into their own hands. The law, in this case, is more about what the social response should be once a killing has occurred. Should there be compensation? Punishment? What form should it take?

Every society needs some system to restore order and a sense of justice.

Skeptic: Is this why we need laws that are enforced regularly, fairly, justly, and consistently, so people don’t feel the need to take matters into their own hands?

FP: I’d put it a bit more broadly: we need systems of justice, which can include mediation systems. In a village in Ladakh—part of northern India with Tibetan populations where I did fieldwork—they didn’t have written laws, but they had very effective ways of resolving conflicts. They put a lot of pressure on the parties to calm down, shake hands, and settle the dispute. It’s vastly different from the nomads I worked with later in eastern Tibet, who had a very different approach. But both systems were extremely effective, and there was a strong moral sense that people shouldn’t fight or even get angry. It’s easy to look at these practices and say they’re not justice, especially when serious things like injuries, killings, or even rape are settled in this way. But for these villages, maintaining peace and order in the community was paramount, and it worked for them.

Every society needs some system to restore order and a sense of justice. What constitutes justice can vary greatly—sometimes it’s revenge, sometimes it’s about restoring order. Laws can be part of that system, and in complex societies, it becomes much harder to rely on bottom-up systems of mediation or conciliation. That’s where having written laws and judges becomes very useful.

Skeptic: In communities without laws or courts, do they just agree, “Tomorrow we’re going to meet at noon, and we’ll all sit down and talk this out?”

FP: Essentially, yes. In the communities I spent time with, it was the headman’s duty to call a village meeting, and everyone was expected to attend and help resolve the issue. In a small community like that, you absolutely could do it.

Skeptic: And if you don’t show up?

FP: There’s huge social pressure for people to play their part in village politics and contribute to village funds and activities.

Skeptic: And if they don’t, then what? Are they gossiped about, shunned, or shamed?

FP: Yes—all of those things, in various ways.

Skeptic: Let’s talk about religious laws. You mentioned Sharia, and from a Western perspective, it’s often seen as a disaster because it’s been hyped up and associated with terrorism. Can you explain how religious laws differ from secular laws?

FP: I’m wondering how much one can generalize here. I’m thinking of the religious laws of Hindu India, Islamic laws, Jewish laws, and I suppose Canon law in Europe—Christian law. I hesitate to generalize, though.

Skeptic: What often confounds modern minds are the very specific laws in Leviticus—like which food you can eat, which clothes you can wear, and how to deal with adultery, which would certainly seem to concern the affected spouse. But why should the state—or whatever governing laws or body—even care about such specific issues?

FP: This highlights a crucial point. In Jewish, Hindu, and Islamic law, the legal and moral spheres are part of the same domain. A lot of these laws are really about guiding people on how to live moral lives according to dharma, God’s will, or divine command. The distinction we often make between law and religion, or law and morality, doesn’t apply in those contexts. The laws are about instructing people on how to live properly, which can involve family relations, contracts, land ownership, but also prayer and ritual.

As for the laws in Leviticus, they’ve puzzled people for a long time. They seem to be about purity and how Jews should live as good people, following rules of cleanliness, which partly distinguished them from other tribes.

Skeptic: What exactly is Sharia law?

FP: Sharia literally means “God’s path for the world.” It’s not best translated as “law” in the way we understand it. It’s more about following the path that God has laid out for us, a path we can’t fully comprehend but must do our best to interpret. The Quran is a guide, but it doesn’t lay out in detail everything we should do. The early Islamic scholars—who were very important in its formative days—studied the Quran and the Hadith (which tradition maintains records the Prophet’s words and actions) to work out just how Muslims should live according to God’s command. They developed texts called fiqh, which are what we might call legal texts, going into more detail about land ownership, commercial activities, legal disputes, inheritance, and charitable trusts.

Islamic law has very little to say about crime.

Islamic law has very little to say about crime. That’s one misconception. People tend to think it’s all about harsh punishments, but the Quran mentions crime only briefly. That was largely the business of the caliphs—the rulers—who were responsible for maintaining law and order. Sharia is much more concerned with ritual and morality, and with civil matters like inheritance and charitable trusts.

Skeptic: Much of biblical legal and moral codes have changed over time. Christianity went through the Enlightenment. But Islam didn’t seem to go through a similar process. Is that a fair characterization?

FP: I’d say that’s partly right. But I’ve never thought about it in exactly those terms. In any legal tradition, there’s resistance to change—that’s kind of the point of law. It’s objective and fixed, so any change requires deep thought. In the Islamic world, there’s been a particularly strong sense that it’s not for people to change or reinterpret God’s path. The law was seen as something fixed.

But in practice, legal scholars, called muftis, were constantly adapting and changing legal practices to suit different contexts and environments. That’s one of the real issues today—Islamic law has become a symbol of resistance to the West, appealing to fundamentalism by going “back to the beginning.”

Skeptic: Let’s talk about stateless law of tribes, villages, networks, and gangs. For example, we tend to think of pirates as lawless, chaotic psychopaths who just randomly raided commerce and people. But, in fact, they were pretty orderly. They had their own constitutions. Each ship had a contract that everyone had to sign, outlining the rules. There’s even this interesting analysis of the Jolly Roger (skull and crossbones) flag. Why fly that flag and alert another ship that you’re coming? In his book The Invisible Hook: The Hidden Economics of Pirates, the economist Peter Leeson argued that it is a signal: “We’re dangerous pirates, and we’re coming to take your stuff, so you might as well hand it over to us, and we won’t kill you.” It’s better for the pirates because they can get the loot without the violence, and it’s better for the victims because they get to keep their lives. Occasionally, you do have to be brutal and make sure your reputation as a badass pirate gets a lot of publicity, so people know that when they see the flag, they should just surrender. But overall, it was a pretty orderly system.

FP: Yes, but it’s only kind of organized. That’s the point. For example, in The Godfather Don Corleone was essentially making up his own rules, using his power to tell others what he wanted. That’s the nature of the Mafia—yes, they had omertà (the rule of silence) and rules about treating each other’s wives with respect, but these rules were never written down. Alleged members who went on trial even denied—under oath—that any kind of organization or rules existed. This was particularly true with the Sicilian Mafia. The denial served two purposes: first, it protected them from outside scrutiny, and second, it allowed powerful figures like Don Corleone—or the real-life Sicilian bosses—to bend the rules whenever they saw fit. If the rules aren’t written down, it’s harder to hold them accountable. They can simply break the rules and impose their will.

Skeptic: Let’s discuss international law. In 1977, David Irving published Hitler’s War, in which he claimed that Hitler didn’t really know about the Holocaust. Rather, Irving blamed it on Himmler specifically, and other high-ranking Nazis in general, along with their obedient underlings. Irving even offered $1,000 to anyone who could produce an order from Hitler saying, “I, Adolf Hitler, hereby order the extermination of European Jewry.” Of course, no such order exists. This is an example of how you shift away from a legal system. The Nazis tried to justify what they were doing with law, but at some point, you can’t write down, “We’re going to kill all the Jews.” That can’t be a formal law.

FP: Exactly. Nazi Germany had a complex legal case, and I’m not an expert on it, but you can see at least a couple legal domains at play. First, they were concerned with international law, especially in how they conducted warfare in the Soviet Union. They at least tried to make a show of following international laws of war. Second, operationally, they created countless laws to keep Germany and the war effort functioning. They used law instrumentally. But when they felt morally uncomfortable with what they were doing, the obvious move was to avoid writing anything down. If it wasn’t documented, it wasn’t visible, and so it became much harder to hold anyone accountable.

Nazi Germany had a complex legal case. Operationally, they created countless laws to keep Germany and the war effort functioning. They used law instrumentally.

Skeptic: During the Nuremberg trials, the defense’s argument was often, “Well, we lost, but if we had won, this would have been legal.” So they claimed it wasn’t fair to hold these trials since they violated the well-established principle of ex post facto, because there was no international law at the time. National sovereignty and self-determination was the norm, so they were saying, in terms of the law of nations, “We were just doing what we do, and it’s none of your business.”

View from above of the judges' bench at the International Military Tribunal in Nuremberg. (Source: National Archives and Records Administration, College Park.)

FP: Legally speaking, the Nuremberg trials were both innovative and hugely problematic. The court assumed the power to sit in judgment on what the leaders of independent nation-states were doing within their borders, or at least largely within their borders (the six largest Nazi death camps were in conquered Poland). But it was revolutionary in terms of developing the concepts of genocide, crimes against humanity, and the reach of international law with a humanitarian focus. So yes, it was innovative and legally difficult to justify, but I don’t think anyone involved felt there was any question that what they were doing was the right thing.

Skeptic: It also established the legal precedent that, going forward, any dictator who commits these kinds of atrocities—if captured—would be held accountable.

FP: Exactly. And that eventually led to the movement that set up the International Criminal Court, where Slobodan Milošević was prosecuted, along with other leaders. Although, it’s extremely difficult to bring such people to trial, and ultimately, the process can be more symbolic than practical.

Is the existence of the International Criminal Court really going to stop someone from committing mass atrocities? I doubt it. But it does symbolize to the world that genocide and other heinous crimes will be called out, and people must be held accountable. In a way, it represents the wider moral world we want to live in and the standards we expect nations to uphold.

Skeptic: Skeptic once asked Elon Musk: “When you start the first Mars colony, what documents would you recommend using to establish a governing system? The U.S. Constitution, the Bill of Rights, the Universal Declaration of Human Rights, the Humanist Manifesto, Atlas Shrugged, or Against the State, an anarcho-capitalist manifesto?” He responded with, “Direct democracy by the people. Laws must be short, as there is trickery in length. Automatic expiration of rules to prevent death by bureaucracy. Any rule can be removed by 40 percent of the people to overcome inertia. Freedom.”

FP: What a great, specific response! He’s really thought about this. Those are some interesting ideas, and I agree that there’s a lot to be said for direct democracy. The main problem with direct democracy, however, is that when you have too many people it becomes cumbersome. How do you gather everyone in a sensible way? The Athenians and Romans had huge assemblies, which created a sense of equality, and that’s valuable. Another thing I would do, which I’ve discussed with a colleague of mine, Al Pashar, is to rotate positions of power. She did research in Indian villages, and I’ve done work with Tibetans in Ladakh, and we found they had similar systems where every household provided a headman or headwoman in turn.

Rotating power is effective at preventing individuals from concentrating too much power.

You might think rotating leadership wouldn’t work, because some people aren’t good leaders, while others are. Wouldn’t it be better to elect the best person for the job? But we found that rotating power is effective at preventing individuals from concentrating too much power. Yes, it’s good to have competent leaders, but when their family or descendants form an elite, you get a hierarchy and bureaucracy. Rotating power prevents that. That’s what I would do in terms of a political system.

As for laws, I’m less concerned with their length, as long as they are accessible and visible for everyone to read and reference. What’s important is having essential laws clearly posted for all to see. And there should be a good system for resolving disputes—perhaps mediation and conciliation rather than a lot of complex laws, with just a few laws in the background.

Skeptic: We’ll send this to Elon, and maybe he’ll hire you to join his team of social engineers.

FP: Although I’m not sure I want to go to Mars, I’d be happy to advise from the comfort of Oxford!

The Moon's getting to be a popular place. Firefly's Blue Ghost touched down on March 2nd in Mare Crisium. It's the first privately built lander to land safely and begin its mission. The little spacecraft set down safely in an upright, stable position and sent back an "I'm here" signal right away.

So far, in the context of 1920s quantum physics, I’ve given you a sense for what an ultra-microscopic measurement consists of, and how one can make a permanent record of it. [Modern (post-1950s) quantum field theory has a somewhat different picture; please keep that in mind. We’ll get to it later.] Along the way I’ve kept the object being measured very simple: just an incoming projectile with a fairly definite motion and moderately definite position, moving steadily in one direction. But now it’s time to consider objects in more interesting quantum situations, and what it means to measure them.

The question for today is: what is a quantum superposition?

I will show you that a quantum superposition of two possibilities, in which the wave function of a system contains one possibility AND another at the same time, does not mean that both possibilities occur; it means that one OR the other may occur.

Instead of a projectile that has a near definite motion, as we’ve considered in recent posts, let’s consider a projectile that is in a quantum superposition of two possible near-definite motions:

• maybe it is moving to the left at a near-definite speed, or
• maybe it is moving to the right at a similar near-definite speed.

This motion is along the x-axis, the coordinate of a one-dimensional physical space. If the projectile is isolated from the rest of the world, we can write a wave function for it alone, which might initially look like

Fig. 1: The wave function of the projectile at the initial time, with two peaks about to head in opposite directions; see Fig. 2.

in which case its evolution over time will look like this:

Fig. 2: The evolution of the isolated projectile’s wave function.

Again I emphasize this is not the wave function of two particles, despite what you might intuitively guess. This is the wave function of a single particle in a superposition of two possible behaviors. For a similar example that we’ll return to in a few weeks, see this post.

Because the height and speed of the two peaks is the same, there is a left-to-right symmetry between them. We can therefore conclude, before we even start, that there’s a 50-50 chance of the particle going right versus going left. More generally, whatever we observe to the left (x<0) will happen with the same probability as what we observe to the right (x>0).

Today I will show you that even though the wave function has one peak moving to the left AND one peak moving to the right, nevertheless this wave function does not describe a projectile that is moving to the left AND moving to the right. Instead, it means that the projectile is moving to the left OR moving to the right. Superposition is an OR, not an AND. In other words, in pre-quantum language, we have either

Fig. 4: The pre-quantum view of the wave function in Figs. 1 and 2; either possibility may occur.

We never have both.

But don’t take my word for it. Let’s see how quantum physics actually works.

First Measurement: A Ball to the Left

Our first goal: to detect the projectile if it is moving to the left.

Let’s start by doing almost the same thing we did in this post, which you may want to read first in order to understand the pictures and the strategy that I’ll present below. To do this, we’ll put a measurement ball on the left, which the projectile will strike if it is moving to the left.

Since we now have a system of two objects rather than one, the space of possibilities for the system now has to be two-dimensional, to include both the position x1 of the projectile and the position x2 of the ball. This now requires us to consider a wave function for not just the projectile alone, as we did in Figs. 1 and 2, but for the projectile and the ball together. This wave function will give us probabilities for each possible arrangement of the projectile and ball — for each choice of x1 and x2.

We’ll put the ball at x2 = -1 initially — to the left of the projectile initially — so that the initial wave function looks like Fig. 4, which shows its absolute value squared as a function of x1 and x2.

Figure 4: The absolute square of the wave function for the projectile (with position x1 near zero) in a superposition of states as in Fig. 1, and the ball which stands ready at position x2=-1 (to the projectile’s left in physical space.)

This wave function has the same shape in x1 as the wave function in Fig. 1, but now centered on the line x2=-1. A collision between projectile and ball will become likely when a peak of the wave function approaches the point x1=x2=-1.

As usual, let’s try to think about this in a pre-quantum language first. If I’m right about wave functions, we have two options:

• The projectile is heading to the left and the measurement ball will react OR
• The projectile is heading to the right and the measurement ball will not react.

Since our wave function is left-to-right symmetric, each option is equally likely, and so if we do this experiment repeatedly, we should see the ball react about half the time.

Here are the two pre-quantum options shown in the usual way, with

• a picture in physical space on the left, and
• a picture of the same event in the space of possibilities on the right.

In the first possibility (Fig. 5a), the projectile moves left, strikes the ball, and the ball recoils to the left. As the ball moves to the left in physical space, the system moves down (toward more negative x2) in the space of possibilities.

Figure 5a: As viewed from physical space (left) and the space of possibilities (right), the projectile moves left and strikes the ball, after which the ball moves left. The ball thus measures the leftward motion of the projectile. The dashed orange line indicates where a collision can occur.

OR

Figure 5a: As viewed from physical space (left) and the space of possibilities (right), the projectile moves right, leaving the ball unscathed. The ball thus measures the rightward motion of the projectile. The dashed orange line indicates where a collision can occur.

In the second possibility (Fig. 5b), the projectile moves right and the ball remains unscathed; in this case, viewed in the space of possibilities, x2 remains at -1 during the entire process while x1 changes steadily toward more positive values.

What about in quantum physics? The wave function should include both options in Figs. 5a and 5b.

Here is an actual solution to the Schrödinger wave equation, showing that this is exactly what happens (and it has more details than the sketches I’ve been doing in my measurement posts, such as this one or this one.) The two peaks spread out more quickly than in my sketches (and I have consequently adjusted the vertical axis as time goes on so that the two bumps remain easily visible.) But the basic prediction is correct: there are indeed two peaks, one moving like the pre-quantum system in Fig 5a, changing direction and moving toward more negative x2, and the other moving like the pre-quantum system in Fig. 5b, moving steadily toward more positive x1.

Figure 6: Actual solution to Schrödinger’s wave equation, showing the absolute square of the wave function beginning with Fig. 4. Notice how the right-moving peak travels steadily toward more positive x1, as in Fig. 5b, while the left-moving peak shows signs of the collision and the subsequent motion of the system toward more negative x2, as in Fig. 5a.

Importantly, even though the system’s wave function displays both possibilities to us at the same time, there is no sense in which the system itself can be in both possibilities at the same time. The system has a near-50% probability of being observed to be within the first peak, near-50% probability of being observed to be within the second, and exactly 0% probability of being observed within both.

Second Measurement: A Ball to the Right

Now let’s put a ball to the right instead, at x=+1. This is a different ball from the previous (we’ll use both of them in a moment) so I’ll color it differently and call its position x3. The pre-quantum behaviors are the same as before, but with x2 replaced with x3 and with the collision happening at positive values of x1 and x3 instead of negative values of x1 and x2.

Figure 7a: As in Figure 5a, but with the orientation reversed.

OR

Figure 7b: As in Figure 5b, but with the orientation reversed.

The quantum version is just a 180-degree rotation of Fig. 6 with x2 replaced with x3.

Figure 8: The evolution of the absolute-value squared of the wave function in this case; compare to Fig. 6 and to Figs. 7a and 7b. Third Measurement: A Ball on Both Sides

But what happens if we put a ball on the left and a ball on the right? Initially the balls are at x2=-1 and x3=+1. What happens later?

Now there are four logical possibilities for what might happen:

1. The ball on the left responds while the ball on the right does not
2. The ball on the right responds while the ball on the left does not
3. Neither ball responds
4. Both balls respond

Where in the space of possibilities do these four options lie? The four logical possibilities listed above would put the ball’s positions in these four possible places:

• Option 1: x2 < -1 and x3 = +1 (and x1 negative, as in Fig. 5a)
• Option 2: x2 = -1 and x3 > +1 (and x1 positive, as in Fig. 7a)
• Option 3: x2 = -1 and x3 = +1 (and x1 is ???)
• Option 4: x2 < -1 and x3 > +1 (and x1 is ???)

The fact that it is not obvious where to put x1 in the last two options should already make you suscpicious; but just setting their x1 to zero for now, let’s draw where these four options occur in the space of possibilities. In Fig. 9 I’ve drawn the lines x2=-1 and x3=+1 across the box, with option 3 at their crossing point. Option 1 lies below down and to the left of option 3; option 2 is found to the rigt of option 3; and option 4 is found down and to the right.

Figure 9: Where the four options are located, roughly speaking. The lines cross at the location x2=-1, x3=+1. If I’m right, only the two cases where one ball moves will have any substantial probability.

What does the wave function actually do? Can the simple two-humped superposition at the start, analogous to Fig. 4, end up four-humped?

Not in this case, anyway. Fig. 10, which depicts the peaks of the absoulte-value-squared of the wave function only, shows the output of the Schrödinger equation. Compare the result to Fig. 9; there are peaks only for options 1 and 2, in which one ball moves and the other does not.

Figure 10: A plot showing where the absolute-value squared of the wave function is largest as the wave function evolves. The axes are as in Fig. 9. Initially the two peaks move in opposite directions parallel to the x1 axis; then, after the projectile collides with one ball or the other, one peak moves down (to more negative x2) and the other to the right (more positive x3). These correspond to the expected options when one and only one ball moves; see Fig. 9.

With balls on either side of it, the projectile cannot avoid hitting one of them, whether it goes right or left, which rules out option 3. And the wave function does not put a peak at option 4, showing there’s no way the projectile can cause both balls to move. The two peaks in the wave function move only in the x1 direction as the projectile goes left OR right; then the projectile collides with one ball OR the other; then the ball with which it collided moves, meaning that the system moves to more negative x2 (i.e. down in Fig. 10) OR to more positive x3 (i.e. to the right in Fig. 10), just as expected from Fig. 9.

Actually it’s not difficult to get the third option — but we don’t need quantum physics for that!

We simply change the original wave function to contain three possibilities: the projectile moves left, or it moves right, or it doesn’t move at all. If it doesn’t move at all, then neither ball will react, a third option even in pre-quantum physics:

If the projectile were isolated, we would encode this notion in a wave function which looks like this:

and when we include the two balls we would see the wave function with three peaks, one sitting still at the point marked “Neither Ball Moves” in Fig. 9. But this isn’t particularly exciting or surprising, since it’s intuitively obvious that a stationary projectile won’t hit either ball.

Every Which Way

There simply is no wave function you can choose — no initial superposition for the single projectile — which can cause the projectile to collide with both balls. The equations will never let this happen, no matter what initial wave function you feed into them. It’s impossible… because a superposition is an OR, not an AND. There is no way to make the projectile go left AND right — not if it’s a particle in 1920s quantum physics, anyway.

Yes, the wave function itself can have peaks that appear at to be in several places at the same time within the space of possibilities, as in Figs. 6, 8, and 10. But the wave function is not the physical system. The wave function tells us about the probabilities for the system’s possibilities; its peaks are just indicating what the most likely possibilities are.

The system itself can only realize one of the many possibilities — it can only be found (through a later measurement) in one place within the space of possibilities. This is always true, even though the wave function for the system highlights all the most probable possibilities simultaneously.

A particle, in the strict sense of the term, is an object with a position and a momentum, even though we cannot know both perfectly at any moment, thanks to Heisenberg’s uncertainty principle. It can only be measured to be in one place, or can only be measured to be traveling in one direction, at a time. In 1920s quantum physics, these statements apply to an electron, which is viewed as a strict particle, and so it cannot go in two directions at once, nor can it be in two places at once. The fact that we are always somewhat ignorant of where an electron is and/or where it is going, and the fact that quantum physics puts ultimate limitations on our ability to know both simultaneously, do not change these basic conceptual lessons… the lessons of (and for) the 1920s.

In 2006 (yes, it was that long ago – yikes) the International Astronomical Union (IAU) officially adopted the definition of dwarf planet – they are large enough for their gravity to pull themselves into a sphere, they orbit the sun and not another larger body, but they don’t gravitationally dominate their orbit. That last criterion is what separates planets (which do dominate their orbit) from dwarf planets. Famously, this causes Pluto to be “downgraded” from a planet to a dwarf planet. Four other objects also met criteria for dwarf planet – Ceres in the asteroid belt, and three Kuiper belt objects, Makemake, Haumea, and Eris.

The new designation of dwarf planet came soon after the discovery of Sedna, a trans-Neptunian object that could meet the old definition of planet. It was, in fact, often reported at the time as the discovery of a 10th planet. But astronomers feared that there were dozens or even hundreds of similar trans-Neptunian objects, and they thought it was messy to have so many planets in our solar system. That is why they came up with the whole idea of dwarf planets. Pluto was just caught in the crossfire – in order to keep Sedna and its ilk from being planets, Pluto had to be demoted as well. As a sort-of consolation, dwarf planets that were also trans-Neptunian objects were named “plutoids”. All dwarf planets are plutoids, except Ceres, which is in the asteroid belt between Mars and Jupiter.

So here we are, two decades later, and I can’t help wondering – where are all the dwarf planets? Where are all the trans-Neptunian objects that astronomers feared would have to be classified as planets that the dwarf planet category was specifically created for? I really thought that by now we would have a dozen or more official dwarf planets. What’s happening? As far as I can tell there are two reasons we are still stuck with only the original five dwarf planets.

One is simply that (even after two decades) candidate dwarf planets have not yet been confirmed with adequate observations. We need to determine their orbit, their shape, and (related to their shape) their size. Sedna is still considered a “candidate” dwarf planet, although most astronomers believe it is an actual dwarf planet and will eventually be confirmed. Until then it is officially considered a trans-Neptunian object. There is also Gonggong, Quaoar, and Orcus which are high probability candidates, and a borderline candidate, Salacia. So there are at least nine, and possibly ten, known likely dwarf planets, but only the original five are confirmed. I guess it is harder to observe these objects than I assumed.

But I have also come across a second reason we have not expanded the official list of dwarf planets. Apparently there is another criterion for plutoids (dwarf planets that are also trans-Neptunian objects) – they have to have an absolute magnitude less than +1 (the smaller the magnitude the brighter the object). Absolute magnitude means how bright an object actually is, not it’s apparent brightness as viewed from the Earth. Absolute magnitude for planets is essentially the result of two factors – size and albedo. For stars, absolute magnitude is the brightness as observed from 10 parsecs away. For solar system bodies, the absolute magnitude is the brightness if the object were one AU from the sun and the observer.

What this means is that astronomers have to determine the absolute magnitude of a trans-Neptunian object before they can officially declare it a dwarf planet. This also means that trans-Neptunian objects that are made of dark material, even if they are large and spherical, may also fail the dwarf planet criteria. Some astronomers are already proposing that this absolute magnitude criterion be replaced by a size criterion – something like 200 km in diameter.

It seems like the dwarf planet designation needs to be revisited. Currently, the James Webb Space Telescope is being used to observe trans-Neptunian objects. Hopefully this means we will have some confirmations soon. Poor Sedna, whose discovery in 2003 set off the whole dwarf planet thing, still has not yet been confirmed.

The post Where Are All the Dwarf Planets? first appeared on NeuroLogica Blog.

In a record-breaking test, researchers remotely detected radioactive material by shooting it with infrared laser pulses and analysing how the light scattered

A supermassive black hole that doesn't appear to be where we would expect seems to be travelling at more than a thousand kilometres per second – the result of a giant cosmic collision

It is impossible for us to know exactly how another person's experience of the world compares to our own, but a new experiment is helping to reveal that colour is indeed a shared phenomenon

The dividing line between gas giant planets and failed stars is blurry at best. The isolated planetary-mass object SIMP J013656.5+093347.3 could be either one. The distinction is largely semantic. However we choose to label and define it, the object displays a surprisingly complex atmosphere for an isolated object without any stellar energy input.

"Journalist" Paul Thacker defends Dr. Jay Bhattacharya and the Great Barrington Declaration by rehashing the same old deceptive rhetoric.

The post Paul Thacker relitigates criticisms of Dr. Jay Bhattacharya and the Great Barrington Declaration first appeared on Science-Based Medicine.

A team of researchers created Morpho, an open-source programmable environment that enables researchers and engineers to conduct shape optimization and design for soft materials. Applications can be for anything from artificial hearts to robot materials that mimic flesh and soft tissue.

A team of researchers created Morpho, an open-source programmable environment that enables researchers and engineers to conduct shape optimization and design for soft materials. Applications can be for anything from artificial hearts to robot materials that mimic flesh and soft tissue.

Researchers have explored the interplay between gravitational effects and quantum interactions in optical atomic clocks, revealing more about quantum entanglement in precision timekeeping.

Within the next decade, space agencies plan to bring samples of rock from Mars to Earth for study. Of concern is the possibility these samples contain life, which could have unforeseen consequences. Therefore, researchers in this field strive to create methods to detect life. Researchers have now successfully demonstrated a method to detect life in ancient rocks analogous to those found on Mars.

Sea ice cover in both the Antarctic and Arctic remained far below average throughout February as global average temperatures linger near record highs

It’s not at all clear that clothes make the man, or woman. However, it is clear that although animals don’t normally wear clothes (except when people dress them up for their own peculiar reasons), living things are provided by natural selection with a huge and wonderful variety. Their outfits involve many different physical shapes and styles, and they arise through various routes. For now, we’ll look briefly just at eye-catching color among animals, and the two routes by which evolution’s clothier dresses them: sexual selection and warning coloration.

Human observers are understandably taken with the extraordinary appearance of certain animals, notably birds, as well as some amphibians and insects, and, in most cases, the dressed-up elegance of males in particular. In 1860, Darwin confessed to a fellow biologist that looking at the tail of a peacock made him “sick.” Not that Darwin lacked an aesthetic sense, rather, he was troubled that his initial version of natural selection didn’t make room for animals having one. After all, the gorgeous colors and extravagant length of a peacock’s tail threatened what came to be known (by way of Herbert Spencer) as “survival of the fittest,” because all that finery seemed to add up to an immense fitness detriment. A long tail is not only metabolically expensive to grow, but it’s more liable to get caught in shrubbery, while the spectacular colors make its owner more conspicuous to potential predators.

Eventually, Darwin arrived at a solution to this dilemma, which he developed in his 1871 book, The Descent of Man and Selection in Relation to Sex. Although details have been added in the ensuing century and a half, his crashing insight—sexual selection—has remained a cornerstone of evolutionary biology.

Sexual selection is sometimes envisaged as different from natural selection, but it isn’t.

Sexual selection is sometimes envisaged as different from natural selection, but it isn’t. Natural selection is neither more nor less than differential reproduction, particularly of individuals and, thereby, genes. It operates in many dimensions, such as obtaining food, avoiding predators, surviving the vagaries of weather, resisting pathogens, and so on. And yet more on! Sexual selection is a subset of natural selection that is so multifaceted and, in some ways, so counterintuitive that it warrants special consideration, as Darwin perceived and subsequent biologists have elaborated.

The bottom line is that in many species, bright coloration—seemingly disadvantageous because it is both expensive to produce and also carries increased risk because of its conspicuousness— nonetheless can contribute to fitness insofar as it is preferentially chosen by females. In such cases, the upside of conspicuous colors increasing mating opportunities compensates for its downsides.

Bright coloration is both expensive to produce and also carries increased risk because of its conspicuousness.

Nothing in science is entirely understood and locked down, but biologists have done a pretty good job with sexual selection. A long-standing question is why, when the sexes are readily distinguishable (termed, sexual dimorphism) it is nearly always the males that are brightly colored. An excellent answer comes from the theory of parental investment, first elaborated by Robert Trivers. The basic idea is that the fundamental biological difference between males and females is not in their genitals but in the defining difference between males and females, namely, how much they invest when it comes to producing offspring. Males are defined as the sex that makes sperm (tiny gametes that are produced in prodigious numbers), while females are egg makers (producing fewer gametes and investing substantially more time and energy on each one).

Sexual selection is responsible for much of the organic world’s Technicolor drama.

As a result, males are often capable of inseminating multiple females because their parental investment in each reproductive effort can be minimal. And so, males in many species, perhaps most, gain an evolutionary advantage by mating with as many females as possible. Because nearly always there are equal numbers of males and females—an important and well-researched statistical phenomenon that deserves its own treatment—this sets up two crucial dynamics. One is male-male competition whereby males hassle with each other for access to the limiting and valuable resource of females and their literal mother load of parental investment. This in turn helps explain the frequent pattern whereby males tend to be more aggressive and outfitted with weapons and an inclination to use them.

The other dynamic, especially important for understanding the evolution of conspicuous male coloration, is female choice (known as epigamic selection). Because females are outfitted with their desirable payload of parental investment, for which males compete, females often (albeit not always) have the opportunity to choose among eager suitors. And they are disposed to go for the brightest, showiest available.

Darwin intuited this dynamic but was uncomfortable about it because at the time, it was felt that aesthetic preferences were a uniquely human phenomenon, not available to animals. Now we know better, in part because the mechanism of such preferences is rather well understood. Sexual selection is responsible for much of the organic world’s Technicolor drama, such as the red of male cardinals, the tails of peacocks, or the rainbow rear ends of mandrill monkeys, all of which make these individuals more appealing to potential mates—probably because, once they are sexually attractive, they become even more attractive according to what evolutionary biologists call the sexy son hypothesis. This involves the implicit genetic promise that females who mate with males who are thus adorned will likely produce sons who will inherit their father’s flashy good looks and will therefore be attractive to the next generation of choosing females, thereby ensuring that the prior generation female who makes such a choice will produce more grandchildren through her sexy sons.

There is a strong correlation between the degree of polygyny (number of females mated on average to a given male), or, more accurately, the ratio of variability in female reproductive success to that of males, and the amount of sexual dimorphism: the extent to which males and females of a given species differ physically. The greater the polygyny (e.g., harem size, as in elephant seals) the greater the sexual dimorphism, while monogamous species tend to be comparatively monomorphic, at least when it comes to body size and weaponry.

In most cases, female reproductive success doesn’t vary greatly among individuals, testimony to the impact of the large parental investment they provide. Female success is maximal when they get all their eggs fertilized and their offspring successfully reared, a number that typically doesn’t differ greatly from one female to another. By contrast, because of their low biologically-mandated parental investment, some males have a very large number of surviving offspring—a function of their success in male-male competition along with female choice—while others are liable to die unsuccessful, nonreproductive, typically troublemaking bachelors.

When it comes to sexual dimorphism in coloration, some mysteries persist.

When it comes to sexual dimorphism in coloration, however, some mysteries persist. Among some socially monogamous species (e.g., warblers), males sport brilliant plumage. This conundrum has been resolved to some extent by the advent of DNA fingerprinting, which has shown that social monogamy doesn’t necessarily correlate with sexual monogamy. Although males of many species have long been known to be sexually randy, verging on promiscuous, females were thought to be more monogamously inclined. However, we now know that females of many species also look for what is termed extra-pair copulations, and it seems likely that this, in turn, has selected for sexy male appearance, which outfits them to potentially take advantage of any out-of-mateship opportunities.

It still isn’t clear why and how such a preference began in the case of particular species (and why it is less developed, or, rarely, even reversed in a few), but once established it becomes what the statistician and evolutionary theorist R.A. Fisher called a “runaway process.” Furthermore, we have some rather good ideas about how this process proceeds.

One is that being impressively arrayed is an indication of somatic and genetic health, which further adds to the fitness payoff when females choose these specimens. Being brightly colored has been shown to correlate with disease resistance, relative absence of parasites, being an especially adroit forager, and the like. In most cases, brightness is physiologically difficult to achieve, which means that dramatic coloration can indicate that such living billboards are also advertising their metabolic muscularity, indicating that they’d likely contain good genetic material as well.

Being brightly colored has been shown to correlate with disease resistance, relative absence of parasites, and being an especially adroit forager.

Another, related hypothesis was more controversial when first proposed by Israeli ornithologist Amotz Zahavi, but has been increasingly supported. This is the concept of “selection for a handicap,” which acknowledges that such traits as bright coloration may well be a handicap in terms of a possessor’s survival. However, Zahavi’s “Handicap Principle” turns a seeming liability into a potential asset insofar as certain traits can be positive indicators of superior quality if their possessors are able to function effectively despite possessing them. It’s as though someone carried a 50-pound backpack and was nonetheless able to finish a race, and maybe even win it! An early criticism of this notion was that the descendants of such handicapped individuals would also likely inherit the handicap, so where’s the adaptive payoff accruing to females who choose to mate with them?

For one, there’s the acknowledged benefit of producing sons who will themselves be preferentially chosen—an intriguing case in which choosy females are more fit not through their sons, but by their grandchildren by way of those sons. In addition, there is the prospect that the choosing female’s daughters would be bequeathed greater somatic viability without their brothers’ bodily handicap. It’s counterintuitive to see bright coloration as a handicap, just as it’s counterintuitive to see a handicap as a potential advantage … but there’s little reason to trust our intuition in the face of nature’s often-confusing complexity.

There’s plenty more to the saga of sexual selection and its generation of flashy animal Beau Brummels, including efforts to explain the many exceptions to the above general patterns. It’s not much of a mystery why mammals don’t partake of flashy dress patterns, given that the class Mammalia generally has poor color vision. But what about primates, who tend to be better endowed? And what of Homo sapiens? Our species sports essentially no genetically-mediated colorful sexual dimorphism. If anything, women tend to be more elaborately adorned than men, at least in Western traditions, a gender difference that seems entirely culture-based. Moreover, among some non-Western social groups, the men get dressed up far more than the women. Clearly, there is much to be resolved, and not just for nonhuman animals.

For another look at dramatic animal patterning, let’s turn to the inverse of sexual attraction, namely, selection for being avoided.

Among the most dramatic looking animals are those whose appearance is “designed” (by natural selection) to cause others—notably predators—to stay away. An array of living things, including some truly spectacular specimens, are downright poisonous, not just in their fangs or stingers but in their very bodies. When they are caterpillars, monarch butterflies feed exclusively on milkweed plants, which contain potent chemical alkaloids that taste disgusting and cause severe digestive upset to animals—especially birds— that eat them, or just venture an incautious nibble.

In the latter case, most birds with a bellyache avoid repeating their mistake although this requires, in turn, that monarchs be sufficiently distinct in their appearance that they carry an easily recognized warning sign. Hence, their dramatic black and bright orange patterning. To the human eye, they are quite lovely. To the eyes of a bird with a terrible taste in its mouth and a pain in its gut, that same conspicuous black and orange is memorable as well, recalling a meal that should not be repeated. It exemplifies “warning coloration,” an easily recalled and highly visible reminder of something to avoid. (It is no coincidence that school buses, ambulances, and fire trucks are also conspicuously colored, although here the goal is enhanced visibility per se, not advertising that these vehicles are bad to eat!)

It is no coincidence that school buses, ambulances, and fire trucks are also conspicuously colored.

The technical term for animal warning signals is aposematic, derived by combining the roots for “apo” meaning away (as in apostate, someone who moves away from a particular belief system) and “sema” meaning signal (as in semaphore). Unpalatable or outright poisonous prey species that were less notable and thus easily forgotten will have achieved little benefit from their protective physiology. And of course, edible animals that are easily recognized would be in even deeper trouble. The adaptive payoff of aposematic coloration even applies if a naïve predator kills a warningly-colored individual, because such sacrifice is biologically rewarded through kin selection when a chastened predator avoids the victim’s genetic relatives.

Many species of bees and wasps are aposematic, as are skunks: once nauseated, or stung, or subjected to stinky skunk spray, twice shy. However, chemically-based shyness isn’t the only way to train a potential predator. Big teeth or sharp claws could do the trick, just by their appearance, without any augmentation. Yet when the threat isn’t undeniably baked into an impressive organ—for example, when it is contained within an animal’s otherwise invisible body chemistry—that’s where a conspicuous, easy-to-remember appearance comes in.

Bright color does triple duty, not only warning off predators and helping acquire mates, but also signaling that brighter and hence healthier individuals are more effective fighters.

Some of the world’s most extraordinary painterly palettes (at least to the human eye) are flaunted by neotropical amphibians known as “poison arrow frogs,” so designated because their skin is so lethally imbued that indigenous human hunters use it to anoint their darts and arrow points. There is no reason, however, for the spectacular coloration of these frogs to serve only as a warning to potential frog-eating predators. As with other dramatically accoutered animals, colorfulness itself often helps attract mates, and not just by holding out the prospect of making sexy sons. Moreover, it has been observed in at least one impressively aposematic amphibian—the scrumptious-looking but highly toxic strawberry poison frog—that bright color does triple duty, not only warning off predators and helping acquire mates, but also signaling to other strawberry poison frogs that brighter and hence healthier individuals are more effective fighters.

Warning coloration occurs in a wide range of living things, evolving pretty much whenever one species develops a deserved reputation for poisonousness, ferocity, or some other form of legitimate threat. Once established, it also opens the door to further evolutionary complexity, including Batesian mimicry, first described in detail by the nineteenth-century English naturalist Henry Walter Bates who researched butterflies in the Amazon rainforest. He noticed that warningly-colored species serve as models, which are then copied by mimics that are selected to piggyback on the reputation established by the former. Brightly banded coral snakes (venomous) are also mimicked, albeit imperfectly, by some species of (nonpoisonous) king snakes. Bees and wasps, with their intimidating stings, have in most cases evolved distinctive color patterns, often bands of black and yellow; they, in turn, are mimicked by a number of other insects that are outfitted with black and yellow bands though they are stingless.

The honestly-clothed signaler can become a model to be mimicked by other species that may not be dangerous to eat but are mistaken for the real (and toxic) McCoy

In short, the honestly-clothed signaler can become a model to be mimicked by other species that may not be dangerous to eat but are mistaken for the real (and toxic) McCoy. Those monarch butterflies, endowed with poisonous, yucky-tasting alkaloids, are mimicked by another species—aptly known as “viceroys” (substitute monarchs)—that bypass the metabolically expensive requirement of dealing with milkweed toxins while benefiting by taking advantage of the monarch’s legitimately acquired reputation.

The plot thickens. Viceroy butterflies (the mimic) and monarchs (the model) can both be successful as long as the mimics aren’t too numerous. A problem arises, however, when viceroys become increasingly abundant, because the more viceroys, the more likely it is that predators will nibble on those harmless mimics rather than being educated by sampling mostly monarchs and therefore trained to avoid their black-and-orange pattern. As a result, the well-being of both monarchs and viceroys is diminished in direct proportion as the latter become abundant, which in turn induces selection of monarchs that are discernibly different from their mimics so as not to be tarred with viceroys’ innocuousness. But the process isn’t done. As the models flutter away from their mimics, the latter can be expected to pursue them, in an ongoing process of evolutionary tag set in motion by the antipredator adaptation represented by the model’s warning coloration, the momentum of which is maintained by the very different challenges—to both the mimic and the model—generated by the system itself.

Frequency-dependent selection is a phenomenon in which the evolutionary success of a biological type varies inversely with its abundance.

This general phenomenon is known as “frequency-dependent selection,” in which the evolutionary success of a biological type varies inversely with its abundance: favored when rare, diminishing as it becomes more frequent. It’s as though certain traits carry within them the seeds of their own destruction, or at least, of keeping their numbers in check, either arriving at a balanced equilibrium or by producing a pattern of pendulum-like fluctuations.

Meanwhile, Batesian mimicry isn’t the only copycat clothing system to have evolved. Plenty of black-and-yellow-banded insects, for example, are equipped with stings, although many other warning patterns are clearly available. Different species could have used their unique pattern of colors as well as alternative designs such as spots and blotches instead of the favored black-and-yellow bands. At work here is yet another evolution-based aposematic phenomenon, known as Mu&#x308;llerian mimicry, after the German naturalist Fritz Mu&#x308;ller. In this kind of mimicry, everyone is a model, because different species that are legitimately threatening in their own right converge on the same pattern. Here, the adaptive advantage is that sharing the same warning appearance facilitates learning by predators: it’s easier to learn to avoid one basic warning signal than a variety, different for each species. It had been thought that Batesian and Mu&#x308;llerian mimicry were opposites, with Batesian being dishonest because the mimic is essentially a parasite of its model’s legitimate reputation (those viceroys), whereas Mu&#x308;llerian mimicry exemplifies shared honesty, as with different species of wasps, bees, and hornets, whose fearsome reputations enhance each others.

It is currently acknowledged, however, that often the distinction is not absolute; within a given array of similar-looking Mu&#x308;llerian mimics, for example, not all species are equally honest when it comes to their decorative signaling. The less dangerous representatives are therefore somewhat Batesian. Conversely, among some species, assemblages that have traditionally been thought to involve Batesian mimics—including the iconic monarch–viceroy duo—mimics are often a bit unpleasant in their own right, so both participants are to some degree Mu&#x308;llerian convergers as well.

What to make of all this? In his book, Unweaving the Rainbow, Richard Dawkins gave us some advice, as brilliant as the colors and patterns of the natural world:

After sleeping through a hundred million centuries, we have finally opened our eyes on a sumptuous planet, sparkling with color, bountiful with life. Within decades we must close our eyes again. Isn’t it a noble and enlightened way of spending our time in the sun, to work at understanding the universe and how we have come to wake up in it?

A new seismic study of Singapore could guide urban growth and renewable energy development in the coastal city nation, where 5.6 million residents live within an area of 734 square kilometers.

Bacterial vaginosis, which is caused by bacteria overgrowing in the vagina, can be hard to treat, with women often experiencing recurring symptoms. Now it seems that asking their male sexual partners to use antibiotic pills and cream could be key to tackling the condition

Cement manufacturing and repair could be significantly improved by using biocement-producing bacteria, but growing the microbes at construction sites remains a challenge. Now, researchers report a freeze-drying approach that preserves the bacteria, potentially allowing construction workers to ultimately use powder out of a packet to quickly make tiles, repair oil wells or strengthen the ground for makeshift roads or camps.

Studying the orbits of thousands of exoplanets shows that large planets tend to have elliptical orbits, while smaller planets tend to have more circular orbits. This split coincides with several other classic features in the exoplanet population, such as the high abundance of small planets over large planets and a tendency for giant planets to only form around stars enriched in heavy elements such as oxygen, carbon and iron. The finding points toward two distinct pathways for forming small and large planets.

Antimalarial drug resistance is a pressing issue in combating the spread of malaria worldwide. In a new study, researchers discovered a key process where malarial parasites take up a human blood cell enzyme, which could provide a new approach for antimalarial treatment.