Friday, 31 August 2018
Winged navigators v. Darwin (again).
Migrating Birds Can Find Their Flocks After Many Miles and Days Apart
Carsten Egevang’s study of Arctic terns, highlighted in the Illustra Media documentary Flight: The Genius of Birds, stunned the ornithological world. It was the first time geolocators logged the exact routes of the world travelers, whose annual tour takes them from pole to pole. As geolocators (also called loggers) improve, more species can be studied, increasing our knowledge of migratory behavior. Now, for the first time, a new flight trace shows surprising social interactions en route for a bird that migrates between Europe and Africa.
The European bee-eater (Merops apiaster) is a flashy bird adorned in brilliant shades of rusty red, orange, yellow, and cyan with black highlights on the face. Males and females are similarly colored. Weighing just 2 ounces at a length of 10 to 11 inches, this gregarious bird with a cheerful song covers a lot of territory, looking for bees, wasps, dragonflies, and other insects to eat. Each bird can consume 250 bees a day, but this causes little impact on bee populations (less than 1 percent, according to Wikipedia). The birds catch their prey in flight, but remove the stingers first by banging the insects against hard surfaces before gulping them down.
From Germany to Angola
The migration of M. apiaster takes it between Germany in summer and Angola in winter, a distance of 14,000 km (8,700 miles). This species migrates in small flocks usually ranging from 5 to 39 individuals. But without being able to follow a flock with ultralight aircraft, it is “it has previously been impossible to monitor spatiotemporal group dynamics in small migrating birds.”
Researchers from the Swiss Ornithological Institute, reporting in Current Biology, outfitted 77 Merops birds in 2015, and 92 more in 2016 with loggers. The instruments recorded ambient light for geolocation and atmospheric pressure for altitude. Ten birds were recovered in 2016, and 19 in 2017. The scientists wanted to investigate the following question:
From zebras to monarch butterflies, migratory species undertake some of the most extreme feats of endurance known in the animal kingdom. With the advent of novel tracking technologies, we are gradually completing the picture of where and when they travel. However, without being able to directly observe migration, we have very little knowledge of who might migrate with whom.
From the data, the scientists were able to piece together the routes of each individual, and infer social interactions within the flock. To the researchers’ surprise, some birds could separate from the main flock in small groups, fly thousands of miles apart on another route, and then re-join the main flock up to 5 days later, even though the sub-flocks probably encountered different environmental conditions along the way.
We present the first evidence of a migratory bird flying together with non-kin of different ages and sexes at all stages of the life cycle. In fact, 49% stay together throughout the annual cycle, never separating longer than 5 days at a time despite the ∼14,000-km journey. Of those that separated for longer, 89% reunited within less than a month with individuals they had previously spent time with, having flown up to 5,000 km apart. These birds were not only using the same non-breeding sites, but also displayed coordinated foraging behaviors — these are unlikely to result from chance encounters in response to the same environmental conditions alone. Better understanding of migratory group dynamics, using the presented methods, could help improve our understanding of collective decision making during large-scale movements.
Functional Advantages
The authors speculated about functional advantages for this divide-and-conquer strategy that they call “fission-fusion” events, but did not expect to see unrelated birds cooperating so well.
In conclusion, we find that birds from the same colony do not always follow the same migratory routes but will in fact join with birds from nearby colonies post-breeding to form groups that migrate together. Groups are generally stable during migration. However, if groups separate, they can reunite in the non-breeding grounds to form dynamic groups that repeatedly forage together, sometimes separating for 1–5 days at a time before migrating back to the breeding grounds together. Most surprisingly, these groups showed no age or sex structure and consisted of non-kin. Our research is the first to show such behavior between migratory non-breeding non-kin bird groups, displaying rare spatiotemporal group dynamics more often observed in mammals.
The wonder of this behavior can be appreciated by reversing roles. Imagine the birds running an experiment on humans. They remove all smartphones and electronic devices, outfit them with loggers the people can’t read, and send them through uncharted territory in Africa in small groups of mixed sex and age who don’t know each other, telling them to meet in Germany. Wouldn’t the birds be flabbergasted to watch small groups split off from the main group, hike for a thousand miles on a different route without communication, and then re-join the main group a week later? Even if the humans used ultralight aircraft, it would be astonishing to see them find one another.
It’s not like the terrain has some bottleneck that forces the birds toward a particular narrow flight corridor. Somehow, these birds show a degree of social coordination only previously seen in mammals.
Fission-fusion can occur without individuals being able to “recognize” each other per se. The same individuals could encounter each other again and again at the same site as a result of migratory connectivity, simply because it is the only one available to them at a particular period. Under such circumstances, resource bottlenecks are likely driving group fusion, not social relationships. On the other hand, where resources occur broadly over a large area, animals must coordinate decisions to fuse into a long-term group — especially if they regularly fissure and must find each other again. Only species with high social cognition, such as elephants, dolphins, and bats, have been found to form long-term social bonds by coordinating decisions, despite separations imposed by migration. In birds, long-term social bonds, despite fission-fusion dynamics, have been observed between non-migratory non-kin, migratory kin, or migratory bonded pairs. Long-term social bonds, despite fission-fusion dynamics, are poorly understood in non-kin migratory birds.
Group Formation
What they’re saying is that unrelated birds that don’t migrate are known to form social bonds, and mating pairs can be expected to cooperate during migration. But why would unrelated birds of mixed sex and age do this? There are advantages to cooperation: “Group formation is pivotal in allowing individuals to interact, transfer information, and adapt to changing conditions,” they say. But it also comes with risks:
Migratory species are notable for their propensity to aggregate in large numbers. The stability of migratory groups over time can be important in determining survival, navigational accuracy, migratory speed, transfer of information, and new migratory behaviors. However, migrating with others is not without risk, as it can increase both disease prevalence and resource competition. Group size typically fluctuates over time and space, with individuals coming together and separating; hereafter termed “fission-fusion dynamics”) as they trade off the different benefits and costs of cooperation. Indeed, resource patches are distant, seasonal, and often unpredictable. One slow individual could, for instance, force the entire group to slow down and miss peaks in resource availability, creating conflict. Groups can therefore either compromise to remain together or spilt into subgroups, for example, of different migratory speeds.
These birds appear to have reached an optimal trade-off between benefits and risks. How could such complex behavior arise by mutation and selection? It seems a challenge too daunting for neo-Darwinism. Maybe that’s why the researchers don’t speculate about evolution.
As wonderful as the observed group dynamics have been shown to be, there are other wonders even greater. Try to build a robot that can fly and power itself by capturing and consuming bees. While you’re at it, make it beautiful to look at and able to sing a beautiful song. Fit all that capability into two ounces, and give it software to find a target 9,000 miles away employing optimal group dynamics. Then endow it with the ability to make copies of itself. If you succeeded at all this, would you not be offended to hear some people say it “emerged” by chance?
On the law of noncontradiction.
re to Think About
IV. The Law of Excluded Middle
One logical law that is easy to accept is the law of non-contradiction. This law can be expressed by the propositional formula ¬(p^¬p). Breaking the sentence down a little makes it easier to understand. p^¬p means that p is both true and false, which is a contradiction. So, negating this statement means that there can be no contradictions (hence, the name of the law). In other words, the law of non-contradiction tells us that a statement cannot be both true and false at the same time. This law is relatively uncontroversial, though there have been those who believe that it may fail in certain special cases. However, it does lead us to a logical principle that has historically been more controversial: the law of excluded middle.
The law of excluded middle can be expressed by the propositional formula p_¬p. It means that a statement is either true or false. Think of it as claiming that there is no middle ground between being true and being false. Every statement has to be one or the other. That’s why it’s called the law of excluded middle, because it excludes a middle ground between truth and falsity. So while the law of non-contradiction tells us that no statement can be both true and false, the law of excluded middle tells us that they must all be one or the other. Now, we can get to this law by considering what it means for the law of non-contradiction to be true. For the law of noncontradiction to be true, ¬(p^¬p) must be true. This means p^¬p must be false. Now, we must refer back the truth table definition for a conjunction. What does it take for p ^ ¬p to be false? It means that at least one of the conjuncts must be false. So, either p is false, or ¬p is false. Well, if p is false, then ¬p must be true. And if ¬p is false, then p must be true. So we are left with the disjunction p _ ¬p, which is exactly the formulation I gave of the law of excluded middle. So we have just derived the law of excluded middle from the law of non-contradiction.
What we just did was convert the negation of a conjunction into a disjunction,
by considering what it means for the conjunction to fail. The rule that lets us do this is known as De Morgan’s rule, after Augustus De Morgan. Formally speaking, it tells us that statements of the following two forms are equivalent: ¬(p^q) and ¬p_¬q. If you substitute ¬p for q in the first formula, you will have the law of non-contradiction. So you might want to try doing the derivation yourself. You will, however, need the rule that tells us that p is equivalent to ¬¬p. The point of this exercise, however, was to show that it is possible to derive the law of excluded middle from the law of non-contradiction. However, it is also possible to convince yourself of the truth of the law of excluded middle without the law of non-contradiction.
We can show using the method of truth tables that the disjunctive statement
p _ ¬p is always true. As a point of terminology, a statement that is always true, irrespective of the truth values of its components, is called a tautology. p _ ¬p is a tautology, since no matter what the truth value of p is, p_¬p is always true. We can see this illustrated in the truth table belowp ¬p p _ ¬p
T F T
F T T
You can try constructing a similar truth table to show that the law of non-contradiction is also a tautology. Its truth table is a bit more complicated, though. However, since the law of excluded middle is a tautology, it should hold no matter what the truth value of p is. In fact, it should be true no matter what statement we decide p should represent. So the law of excluded middle tells us that every statement whatsoever must be either true or false. At first, this might not seem like a very problematic claim. But before getting too comfortable with this idea, we might want to consider Bertrand Russell’s famous example: “The present King of France is bald.” Since the law of excluded middle tells us that every statement is either true or false, the sentence “The present King of France is bald” must be either true or false. Which is it?
Since there is no present King of France, it would seem quite unusual to claim that this sentence is true. But if we accept the law of excluded middle, this leaves us only one option - namely, to claim that it is false. Now, at this point, we might choose to reject the law of excluded middle altogether, or contend that it simply does not hold in some cases. This is an interesting option toconsider, but then we might need to consider why the method of constructing truth tables tells us that the law of excluded middle holds, if it actually doesn’t. We would also have to consider why it is derivable from the principle of non-contradiction. After all, this sentence doesn’t pose a problem for the law of non-contradiction, since it’s not both true and false. So we’ll ignore this option for now.
Returning to the problem at hand, we must now consider the question of what it means for the sentence “The present King of France is bald” to be false. Perhaps it means “The present King of France is not bald.” But that would imply that there is a present King of France, and he is not bald. This is not a conclusion we want to reach. Russell, in his 1905 paper “On Denoting” presented his own solution to this problem, which comes in the form of a theory of definite descriptions. Under this theory, we can think of there being a hidden conjunctive structure in the sentence “The present King of France is bald.” What the sentence really says is that there is a present King of France, and he is bald. So the fact that there is no present King of France implies that this sentence is false, and we have the solution we need.
Russell’s solution clearly suggests that we can’t just extract the logical structure of a sentence from its grammatical structure. We have to take other things into account. If you’re interested in issues about the relationship between logic and language, you might want to take a class in philosophy of language. The other essay in this section, entitled “Logic and Natural Language”, covers some other issues in this area.
One method of proof that comes naturally from the law of excluded middle is a proof by contradiction, or reductio ad absurdum. In a proof by contradiction, we assume the negation of a statement and proceed to prove that the assumption leads us to a contradiction. A reductio ad absurdum sometimes shows that the assumption leads to an absurd conclusion which is not necessarily a contradiction. In both cases, the unsatisfactory result of negating our statement leads us to conclude that our statement is, in fact, true. How does this follow from the law of excluded middle? The law of excluded middle tells us that there are only two possibilities with respect to a statement p. Either p is true, or ¬p is true. In showing that the assumption of ¬p leads us to a contradictory conclusion, we eliminate the possibility that ¬p is true. So we are then forced to conclude that p is true, since the law of excluded middle is supposed to hold for any statement whatsoever.
Now, I’ve been a bit flippant in talking about statements. Statements can be about a lot of different things. The above discussion illustrated a problem with statements about things that don’t actually exist. I’m sure most people would agree that the designation “the present King of France” refers to something that doesn’t exist. But what about situations where it’s not so certain? One of the main metaphysical questions in the philosophy of mathematics is the question of whether or not mathematical objects actually exist. Think about the question of whether numbers exist. If they do exist, then what are they? After all, they’re not concrete things that we can reach out and touch. But if they don’t exist, then what’s going on in math?
Metaphysical worries have motivated certain people to argue that proofs by contradiction are not legitimate proofs in mathematics. Proponents of intuitionism and constructivism in mathematics place a significant emphasis on the construction of mathematical objects. One way to characterize this position is that in order to show that a mathematical object exists, it is necessary to construct it, or at the very least, provide a method for its construction. This is their answer to the metaphysical question. Suppose we had a mathematical proof in which we assumed an object did not exist, and proved that our assumption lead us to a contradiction. For an intuitionist or a constructivist, this proof would not be a sufficient demonstration that the object does exist. A sufficient demonstration would have to involve the construction of the object.
Even if questions about existence get too complicated, we can still ask the question “What mathematical objects can we legitimately talk about?” The intuitionist answer is that we can talk about those mathematical objects which we know can be constructed.
Simply speaking, intuitionistic logic is logic without the law of excluded middle. I have outlined some small part of the motivation behind developing such a system, but more details can be found in the work of L.E.J. Brouwer and Arend Heyting.
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