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Carrion Luggage  Native to the Americas, the turkey vulture (Cathartes aura) travels widely in search of sustenance. While usually foraging alone, it relies on other individuals of its species for companionship and mutual protection. Sometimes misunderstood, sometimes feared, sometimes shunned, it nevertheless performs an important role in the ecosystem. This scavenger bird is a marvel of efficiency. Rather than expend energy flapping its wings, it instead locates uplifting columns of air, and spirals within them in order to glide to greater heights. This behavior has been mistaken for opportunism, interpreted as if it is circling doomed terrestrial animals destined to be its next meal. In truth, the vulture takes advantage of these thermals to gain the altitude needed glide longer distances, flying not out of necessity, but for the joy of it. It also avoids the exertion necessary to capture live prey, preferring instead to feast upon that which is already dead. In this behavior, it resembles many humans. It is not what most of us would consider to be a pretty bird. While its habits are often off-putting, or even disgusting, to members of more fastidious species, the turkey vulture helps to keep the environment from being clogged with detritus. Hence its Latin binomial, which translates to English as "golden purifier." I rarely know where the winds will take me next, or what I might find there. The journey is the destination. |
| Nothing bigger than infinity, right? Well, what about second infinity? From Quanta: Mathematicians Measure Infinities and Find Theyâre Equal  Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories. When someone brightly proclaims, "Nothing is impossible!" I have two possible responses, depending on my mood: 1) Even in a vacuum, there exist electromagnetic fields, quantum virtual particles, etc., so yes, technically, it's impossible to achieve "nothing." 2) Okay, if nothing is impossible, please, go ahead and count to infinity. And if I'm in a really bad mood, there's a third: 3) "You are." But despite my #2 response, which demonstrates that there are things that are, in point of fact, not possible, mathematicians understand quite a bit about the very useful (but probably entirely abstract) concept of infinity, one bit being that the infinity of integers is of a lower order, aka smaller, than the infinity of real numbers. The problem was first identified over a century ago. At the time, mathematicians knew that âthe real numbers are bigger than the natural numbers, but not how much bigger. Is it the next biggest size, or is there a size in between?â said Maryanthe Malliaris of the University of Chicago, co-author of the new work along with Saharon Shelah of the Hebrew University of Jerusalem and Rutgers University. Just so we're clear, in math, "natural numbers" means positive integers, and "real numbers" means integers, fractions, and non-repeating transcendental numbers like pi. From what little about this stuff that I understand, there is a greater infinity of real numbers just between the integers 1 and 2 than the entire infinity of integers. Oh, and to make your mind spin even more, the infinity of natural numbers is the same size as the infinity of integers, which is the same size as the infinity of even numbers, which is the same size as the infinity of multiples of 100, and the infinity of prime numbers, and so on. You don't have to take my word for it, but mathematicians have proven this shit rigorously, as the article goes on to explain using pretty basic concepts, all because of the work of a dude named Georg Cantor. Then: What Cantor couldnât figure out was whether there exists an intermediate size of infinity â something between the size of the countable natural numbers and the uncountable real numbers. He guessed not, a conjecture now known as the continuum hypothesis. Now, I'm obviously not a mathematician, but this stuff fascinates me to the point where I've read entire books about it. One of them, as I recall, pointed out later work that showed that the continuum hypothesis cannot be proven or disproven using the framework of mathematics, which this article also nods to: In the 1960s, the mathematician Paul Cohen explained why. Cohen developed a method called âforcingâ that demonstrated that the continuum hypothesis is independent of the axioms of mathematics â that is, it couldnât be proved within the framework of set theory. (Cohenâs work complemented work by Kurt GĂśdel in 1940 that showed that the continuum hypothesis couldnât be disproved within the usual axioms of mathematics.) The article continues in even more detail and, no, there's not a lot of actual math in it; it's mostly written in plain language, and the only problem I had reading it was keeping all the names straight. Because while I don't understand much of mathematics, I understand it better than I understand people. My real point in posting this, however, is to show that some things are, in fact, impossible. But what is possible is to know what's impossible. |
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