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Marc Kaufman…engrossing …At times, Livio's theorems, proofs and conundrums may be challenging for readers who struggled through algebra, but he makes most of this material not only comprehensible but downright intriguing.
—The Washington Post
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Mario Livio is a senior astrophysicist and the Head of the Office of Public Outreach at the Space Telescope Science Institute (STScI) in Baltimore, Maryland. He is the author of The Golden Ratio, a highly acclaimed book about mathematics and art for which he received the International Pythagoras Prize and the Peano Prize, The Equation That Couldn't Be Solved, and The Accelerating Universe. He lives in Baltimore, Maryland.
Mathematicians themselves often insist that their work has no practical effect. The British mathematician G. H. Hardy went so far as to describe his own work this way: "No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world." He was wrong. The Hardy-Weinberg law allows population geneticists to predict how genes are transmitted from one generation to the next, and Hardy's work on the theory of numbers found unexpected implications in the development of codes.
Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
A few years ago, I was giving a talk at Cornell University. One of my PowerPoint slides read: "Is God a mathematician?" As soon as that slide appeared, I heard a student in the front row gasp: "Oh God, I hope not!"
My rhetorical question was neither a philosophical attempt to define God for my audience nor a shrewd scheme to intimidate the math phobics. Rather, I was simply presenting a mystery with which some of the most original minds have struggled for centuries -- the apparent omnipresence and omnipotent powers of mathematics. These are the type of characteristics one normally associates only with a deity. As the British physicist James Jeans (1877-1946) once put it: "The universe appears to have been designed by a pure mathematician." Mathematics appears to be almost too effective in describing and explaining not only the cosmos at large, but even some of the most chaotic of human enterprises.
Whether physicists are attempting to formulate theories of the universe, stock market analysts are scratching their heads to predict the next market crash, neurobiologists are constructing models of brain function, or military intelligence statisticians are trying to optimize resource allocation, they are all using mathematics. Furthermore, even though they may be applying formalisms developed in different branches of mathematics, they are still referring to the same global, coherent mathematics. What is it that gives mathematics such incredible powers? Or, as Einstein once wondered: "How is it possible that mathematics, a product of human thought that is independent of experience [the emphasis is mine], fits so excellently the objects of physical reality?"
This sense of utter bewilderment is not new. Some of the philosophers in ancient Greece, Pythagoras and Plato in particular, were already in awe of the apparent ability of mathematics to shape and guide the universe, while existing, as it seemed, above the powers of humans to alter, direct, or influence it. The English political philosopher Thomas Hobbes (1588-1679) could not hide his admiration either. In Leviathan, Hobbes's impressive exposition of what he regarded as the foundation of society and government, he singled out geometry as the paradigm of rational argument:
Seeing then that truth consisteth in the right ordering of names in our affirmations, a man that seeketh precise truth had need to remember what every name he uses stands for, and to place it accordingly; or else he will find himself entangled in words, as a bird in lime twigs; the more he struggles, the more belimed. And therefore in geometry (which is the only science that it hath pleased God hitherto to bestow on mankind), men begin at settling the significations of their words; which settling of significations, they call definitions, and place them in the beginning of their reckoning.
Millennia of impressive mathematical research and erudite philosophical speculation have done relatively little to shed light on the enigma of the power of mathematics. If anything, the mystery has in some sense even deepened. Renowned Oxford mathematical physicist Roger Penrose, for instance, now perceives not just a single, but a triple mystery. Penrose identifies three different "worlds": the world of our conscious perceptions, the physical world, and the Platonic world of mathematical forms. The first world is the home of all of our mental images -- how we perceive the faces of our children, how we enjoy a breathtaking sunset, or how we react to the horrifying images of war. This is also the world that contains love, jealousy, and prejudices, as well as our perception of music, of the smells of food, and of fear. The second world is the one we normally refer to as physical reality. Real flowers, aspirin tablets, white clouds, and jet airplanes reside in this world, as do galaxies, planets, atoms, baboon hearts, and human brains. The Platonic world of mathematical forms, which to Penrose has an actual reality comparable to that of the physical and the mental worlds, is the motherland of mathematics. This is where you will find the natural numbers 1, 2, 3, 4,..., all the shapes and theorems of Euclidean geometry, Newton's laws of motion, string theory, catastrophe theory, and mathematical models of stock market behavior. And now, Penrose observes, come the three mysteries. First, the world of physical reality seems to obey laws that actually reside in the world of mathematical forms. This was the puzzle that left Einstein perplexed. Physics Nobel laureate Eugene Wigner (1902-95) was equally dumbfounded:
The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
Second, the perceiving minds themselves -- the dwelling of our conscious perceptions -- somehow managed to emerge from the physical world. How was mind literally born out of matter? Would we ever be able to formulate a theory of the workings of consciousness that would be as coherent and as convincing as, say, our current theory of electromagnetism? Finally, the circle is mysteriously closed. Those perceiving minds were miraculously able to gain access to the mathematical world by discovering or creating and articulating a treasury of abstract mathematical forms and concepts.
Penrose does not offer an explanation for any of the three mysteries. Rather, he laconically concludes: "No doubt there are not really three worlds but one, the true nature of which we do not even glimpse at present." This is a much more humble admission than the response of the schoolmaster in the play Forty Years On (written by the English author Alan Bennett) to a somewhat similar question:
Foster: I'm still a bit hazy about the Trinity, sir.
Schoolmaster: Three in one, one in three, perfectly straightforward. Any doubts about that see your maths master.
The puzzle is even more entangled than I have just indicated. There are actually two sides to the success of mathematics in explaining the world around us (a success that Wigner dubbed "the unreasonable effectiveness of mathematics"), one more astonishing than the other. First, there is an aspect one might call "active." When physicists wander through nature's labyrinth, they light their way by mathematics -- the tools they use and develop, the models they construct, and the explanations they conjure are all mathematical in nature. This, on the face of it, is a miracle in itself. Newton observed a falling apple, the Moon, and tides on the beaches (I'm not even sure if he ever saw those!), not mathematical equations. Yet he was somehow able to extract from all of these natural phenomena, clear, concise, and unbelievably accurate mathematical laws of nature. Similarly, when the Scottish physicist James Clerk Maxwell (1831-79) extended the framework of classical physics to include all the electric and magnetic phenomena that were known in the 1860s, he did so by means of just four mathematical equations. Think about this for a moment. The explanation of a collection of experimental results in electromagnetism and light, which had previously taken volumes to describe, was reduced to four succinct equations. Einstein's general relativity is even more astounding -- it is a perfect example of an extraordinarily precise, self-consistent mathematical theory of something as fundamental as the structure of space and time.
But there is also a "passive" side to the mysterious effectiveness of mathematics, and it is so surprising that the "active" aspect pales by comparison. Concepts and relations explored by mathematicians only for pure reasons -- with absolutely no application in mind -- turn out decades (or sometimes centuries) later to be the unexpected solutions to problems grounded in physical reality! How is that possible? Take for instance the somewhat amusing case of the eccentric British mathematician Godfrey Harold Hardy (1877-1947). Hardy was so proud of the fact that his work consisted of nothing but pure mathematics that he emphatically declared: "No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world." Guess what -- he was wrong. One of his works was reincarnated as the Hardy-Weinberg law (named after Hardy and the German physician Wilhelm Weinberg [1862-1937]), a fundamental principle used by geneticists to study the evolution of populations. Put simply, the Hardy-Weinberg law states that if a large population is mating totally at random (and migration, mutation, and selection do not occur), then the genetic constitution remains constant from one generation to the next. Even Hardy's seemingly abstract work on number theory -- the study of the properties of the natural numbers -- found unexpected applications. In 1973, the British mathematician Clifford Cocks used the theory of numbers to create a breakthrough in cryptography -- the development of codes. Cocks's discovery made another statement by Hardy obsolete. In his famous book A Mathematician's Apology, published in 1940, Hardy pronounced: "No one has yet discovered any war-like purpose to be served by the theory of numbers." Clearly, Hardy was yet again in error. Codes have been absolutely essential for military communications. So even Hardy, one of the most vocal critics of applied mathematics, was "dragged" (probably kicking and screaming, if he had been alive) into producing useful mathematical theories.
But this is only the tip of the iceberg. Kepler and Newton discovered that the planets in our solar system follow orbits in the shape of ellipses -- the very curves studied by the Greek mathematician Menaechmus (fl. ca. 350 BC) two millennia earlier. The new types of geometries outlined by Georg Friedrich Bernhard Riemann (1826-66) in a classic lecture in 1854 turned out to be precisely the tools that Einstein needed to explain the cosmic fabric. A mathematical "language" called group theory, developed by the young prodigy Évariste Galois (1811-32) simply to determine the solvability of algebraic equations, has today become the language used by physicists, engineers, linguists, and even anthropologists to describe all the symmetries of the world. Moreover, the concept of mathematical symmetry patterns has, in some sense, turned the entire scientific process on its head. For centuries the route to understanding the workings of the cosmos started with a collection of experimental or observational facts, from which, by trial and error, scientists attempted to formulate general laws of nature. The scheme was to begin with local observations and build the jigsaw puzzle piece by piece. With the recognition in the twentieth century that well-defined mathematical designs underlie the structure of the subatomic world, modern-day physicists started to do precisely the opposite. They put the mathematical symmetry principles first, insisting that the laws of nature and indeed the basic building blocks of matter should follow certain patterns, and they deduced the general laws from these requirements. How does nature know to obey these abstract mathematical symmetries?
In 1975, Mitch Feigenbaum, then a young mathematical physicist at Los Alamos National Laboratory, was playing with his HP-65 pocket calculator. He was examining the behavior of a simple equation. He noticed that a sequence of numbers that appeared in the calculations was getting closer and closer to a particular number: 4.669...To his amazement, when he examined other equations, the same curious number appeared again. Feigenbaum soon concluded that his discovery represented something universal, which somehow marked the transition from order to chaos, even though he had no explanation for it. Not surprisingly, physicists were very skeptical at first. After all, why should the same number characterize the behavior of what appeared to be rather different systems? After six months of professional refereeing, Feigenbaum's first paper on the topic was rejected. Not much later, however, experiments showed that when liquid helium is heated from below it behaves precisely as predicted by Feigenbaum's universal solution. And this was not the only system found to act this way. Feigenbaum's astonishing number showed up in the transition from the orderly flow of a fluid to turbulence, and even in the behavior of water dripping from a tap.
The list of such "anticipations" by mathematicians of the needs of various disciplines of later generations just goes on and on. One of the most fascinating examples of the mysterious and unexpected interplay between mathematics and the real (physical) world is provided by the story of knot theory -- the mathematical study of knots. A mathematical knot resembles an ordinary knot in a string, with the string's ends spliced together. That is, a mathematical knot is a closed curve with no loose ends. Oddly, the main impetus for the development of mathematical knot theory came from an incorrect model for the atom that was developed in the nineteenth century. Once that model was abandoned -- only two decades after its conception -- knot theory continued to evolve as a relatively obscure branch of pure mathematics. Amazingly, this abstract endeavor suddenly found extensive modern applications in topics ranging from the molecular structure of DNA to string theory -- the attempt to unify the subatomic world with gravity. I shall return to this remarkable tale in chapter 8, because its circular history is perhaps the best demonstration of how branches of mathematics can emerge from attempts to explain physical reality, then how they wander into the abstract realm of mathematics, only to eventually return unexpectedly to their ancestral origins.
Discovered or Invented?
Even the brief description I have presented so far already provides overwhelming evidence of a universe that is either governed by mathematics or, at the very least, susceptible to analysis through mathematics. As this book will show, much, and perhaps all, of the human enterprise also seems to emerge from an underlying mathematical facility, even where least expected. Examine, for instance, an example from the world of finance -- the Black-Scholes option pricing formula (1973). The Black-Scholes model won its originators (Myron Scholes and Robert Carhart Merton; Fischer Black passed away before the prize was awarded) the Nobel Memorial Prize in economics. The key equation in the model enables the understanding of stock option pricing (options are financial instruments that allow bidders to buy or sell stocks at a future point in time, at agreed-upon prices). Here, however, comes a surprising fact. At the heart of this model lies a phenomenon that had been studied by physicists for decades -- Brownian motion, the state of agitated motion exhibited by tiny particles such as pollen suspended in water or smoke particles in the air. Then, as if that were not enough, the same equation also applies to the motion of hundreds of thousands of stars in star clusters. Isn't this, in the language of Alice in Wonderland, "curiouser and curiouser"? After all, whatever the cosmos may be doing, business and finance are definitely worlds created by the human mind.
Or, take a common problem encountered by electronic board manufacturers and designers of computers. They use laser drills to make tens of thousands of holes in their boards. In order to minimize the cost, the computer designers do not want their drills to behave as "accidental tourists." Rather, the problem is to find the shortest "tour" among the holes, that visits each hole position exactly once. As it turns out, mathematicians have investigated this exact problem, known as the traveling salesman problem, since the 1920s. Basically, if a salesperson or a politician on the campaign trail needs to travel in the most economical way to a given number of cities, and the cost of travel between each pair of cities is known, then the traveler must somehow figure out the cheapest way of visiting all the cities and returning to his or her starting point. The traveling salesman problem was solved for 49 cities in the United States in 1954. By 2004, it was solved for 24,978 towns in Sweden. In other words, the electronics industry, companies routing trucks for parcel pickups, and even Japanese manufacturers of pinball-like pachinko machines (which have to hammer thousands of nails) have to rely on mathematics for something as simple as drilling, scheduling, or the physical design of computers.
Mathematics has even penetrated into areas not traditionally associated with the exact sciences. For instance, there is a Journal of Mathematical Sociology (which in 2006 was in its thirtieth volume) that is oriented toward a mathematical understanding of complex social structures, organizations, and informal groups. The journal articles address topics ranging from a mathematical model for predicting public opinion to one predicting interaction in social groups.
Going in the other direction -- from mathematics into the humanities -- the field of computational linguistics, which originally involved only computer scientists, has now become an interdisciplinary research effort that brings together linguists, cognitive psychologists, logicians, and artificial intelligence experts, to study the intricacies of languages that have evolved naturally.
Is this some mischievous trick played on us, such that all the human struggles to grasp and comprehend ultimately lead to uncovering the more and more subtle fields of mathematics upon which the universe and we, its complex creatures, were all created? Is mathematics, as educators like to say, the hidden textbook -- the one the professor teaches from -- while giving his or her students a much lesser version so that he or she will seem all the wiser? Or, to use the biblical metaphor, is mathematics in some sense the ultimate fruit of the tree of knowledge?
As I noted briefly at the beginning of this chapter, the unreasonable effectiveness of mathematics creates many intriguing puzzles: Does mathematics have an existence that is entirely independent of the human mind? In other words, are we merely discovering mathematical verities, just as astronomers discover previously unknown galaxies? Or, is mathematics nothing but a human invention? If mathematics indeed exists in some abstract fairyland, what is the relation between this mystical world and physical reality? How does the human brain, with its known limitations, gain access to such an immutable world, outside of space and time? On the other hand, if mathematics is merely a human invention and it has no existence outside our minds, how can we explain the fact that the invention of so many mathematical truths miraculously anticipated questions about the cosmos and human life not even posed until many centuries later? These are not easy questions. As I will show abundantly in this book, even modern-day mathematicians, cognitive scientists, and philosophers don't agree on the answers. In 1989, the French mathematician Alain Connes, winner of two of the most prestigious prizes in mathematics, the Fields Medal (1982) and the Crafoord Prize (2001), expressed his views very clearly:
Take prime numbers [those divisible only by one and themselves], for example, which as far as I'm concerned, constitute a more stable reality than the material reality that surrounds us. The working mathematician can be likened to an explorer who sets out to discover the world. One discovers basic facts from experience. In doing simple calculations, for example, one realizes that the series of prime numbers seems to go on without end. The mathematician's job, then, is to demonstrate that there exists an infinity of prime numbers. This is, of course, an old result due to Euclid. One of the most interesting consequences of this proof is that if someone claims one day to have found the greatest prime number, it will be easy to show that he's wrong. The same is true for any proof. We run up therefore against a reality every bit as incontestable as physical reality.
Martin Gardner, the famous author of numerous texts in recreational mathematics, also takes the side of mathematics as a discovery. To him, there is no question that numbers and mathematics have their own existence, whether humans know about them or not. He once wittily remarked: "If two dinosaurs joined two other dinosaurs in a clearing, there would be four there, even though no humans were around to observe it, and the beasts were too stupid to know it." As Connes emphasized, supporters of the "mathematics-as-a-discovery" perspective (which, as we shall see, conforms with the Platonic view) point out that once any particular mathematical concept has been grasped, say the natural numbers 1, 2, 3, 4,..., then we are up against undeniable facts, such as 32 1 42 5 52, irrespective of what we think about these relations. This gives at least the impression that we are in contact with an existing reality.
Others disagree. While reviewing a book in which Connes presented his ideas, the British mathematician Sir Michael Atiyah (who won the Fields Medal in 1966 and the Abel Prize in 2004) remarked:
Any mathematician must sympathize with Connes. We all feel that the integers, or circles, really exist in some abstract sense and the Platonic view [which will be described in detail in chapter 2] is extremely seductive. But can we really defend it? Had the universe been one dimensional or even discrete it is difficult to see how geometry could have evolved. It might seem that with the integers we are on firmer ground, and that counting is really a primordial notion. But let us imagine that intelligence had resided, not in mankind, but in some vast solitary and isolated jelly-fish, buried deep in the depths of the Pacific Ocean. It would have no experience of individual objects, only with the surrounding water. Motion, temperature and pressure would provide its basic sensory data. In such a pure continuum the discrete would not arise and there would be nothing to count.
Atiyah therefore believes that "man has created [the emphasis is mine] mathematics by idealizing and abstracting elements of the physical world." Linguist George Lakoff and psychologist Rafael Núñez agree. In their book Where Mathematics Comes From, they conclude: "Mathematics is a natural part of being human. It arises from our bodies, our brains, and our everyday experiences in the world."
The viewpoint of Atiyah, Lakoff, and Núñez raises another interesting question. If mathematics is entirely a human invention, is it truly universal? In other words, if extraterrestrial intelligent civilizations exist, would they invent the same mathematics? Carl Sagan (1934-96) used to think that the answer to the last question was in the affirmative. In his book Cosmos, when he discussed what type of signal an intelligent civilization would transmit into space, he said: "It is extremely unlikely that any natural physical process could transmit radio messages containing prime numbers only. If we received such a message we would deduce a civilization out there that was at least fond of prime numbers." But how certain is that? In his recent book A New Kind of Science, mathematical physicist Stephen Wolfram argued that what we call "our mathematics" may represent just one possibility out of a rich variety of "flavors" of mathematics. For instance, instead of using rules based on mathematical equations to describe nature, we could use different types of rules, embodied in simple computer programs. Furthermore, some cosmologists have recently discussed even the possibility that our universe is but one member of a multiverse -- a huge ensemble of universes. If such a multiverse indeed exists, would we really expect the other universes to have the same mathematics?
Molecular biologists and cognitive scientists bring to the table yet another perspective, based on studies of the faculties of the brain. To some of these researchers, mathematics is not very different from language. In other words, in this "cognitive" scenario, after eons during which humans stared at two hands, two eyes, and two breasts, an abstract definition of the number 2 has emerged, much in the same way that the word "bird" has come to represent many two-winged animals that can fly. In the words of the French neuroscientist Jean-Pierre Changeux: "For me the axiomatic method [used, for instance, in Euclidean geometry] is the expression of cerebral faculties connected with the use of the human brain. For what characterizes language is precisely its generative character." But, if mathematics is just another language, how can we explain the fact that while children study languages easily, many of them find it so hard to study mathematics? The Scottish child prodigy Marjory Fleming (1803-11) charmingly described the type of difficulties students encounter with mathematics. Fleming, who never lived to see her ninth birthday, left journals that comprise more than nine thousand words of prose and five hundred lines of verse. In one place she complains: "I am now going to tell you the horrible and wretched plague that my multiplication table gives me; you can't conceive it. The most devilish thing is 8 times 8 and 7 times 7; it is what nature itself can't endure."
A few of the elements in the intricate questions I have presented can be recast into a different form: Is there any difference in basic kind between mathematics and other expressions of the human mind, such as the visual arts or music? If there isn't, why does mathematics exhibit an imposing coherence and self-consistency that does not appear to exist in any other human creation? Euclid's geometry, for instance, remains as correct today (where it applies) as it was in 300 BC; it represents "truths" that are forced upon us. By contrast, we are neither compelled today to listen to the same music the ancient Greeks listened to nor to adhere to Aristotle's naïve model of the cosmos.
Very few scientific subjects today still make use of ideas that can be three thousand years old. On the other hand, the latest research in mathematics may refer to theorems that were published last year, or last week, but it may also use the formula for the surface area of a sphere proved by Archimedes around 250 BC! The nineteenth century knot model of the atom survived for barely two decades because new discoveries proved elements of the theory to be in error. This is how science progresses. Newton gave credit (or not! see chapter 4) for his great vision to those giants upon whose shoulders he stood. He might also have apologized to those giants whose work he had made obsolete.
This is not the pattern in mathematics. Even though the formalism needed to prove certain results might have changed, the mathematical results themselves do not change. In fact, as mathematician and author Ian Stewart once put it, "There is a word in mathematics for previous results that are later changed -- they are simply called mistakes." And such mistakes are judged to be mistakes not because of new findings, as in the other sciences, but because of a more careful and rigorous reference to the same old mathematical truths. Does this indeed make mathematics God's native tongue?
If you think that understanding whether mathematics was invented or discovered is not that important, consider how loaded the difference between "invented" and "discovered" becomes in the question: Was God invented or discovered? Or even more provocatively: Did God create humans in his own image, or did humans invent God in their own image?
I will attempt to tackle many of these intriguing questions (and quite a few additional ones) and their tantalizing answers in this book. In the process, I shall review insights gained from the works of some of the greatest mathematicians, physicists, philosophers, cognitive scientists, and linguists of past and present centuries. I shall also seek the opinions, caveats, and reservations of many modern thinkers. We start this exciting journey with the groundbreaking perspective of some of the very early philosophers.
Copyright © 2009 by Mario Livio
The title of astrophysicist Livio's latest wide-ranging science survey is a teaser since God rarely makes an appearance; along with the French astronomer Laplace, Livio has no need of that "hypothesis." Rather, Livio (The Golden Ratio) is concerned with the contentious question: is mathematics a human invention? Or is it the intricate design of the universe that we are slowly discovering? Scientists in past centuries have argued for the latter, Platonist position. In the last 50 years, however, many scientists, calling into question the whole idea of scientific discovery, maintain that we have invented mathematics. Livio gives as one example the famous golden ratio, which has fascinated Western mathematicians for millennia and was originally emphasized for its mystical symbolism. But Chinese mathematicians, not sharing that outlook, didn't discover it-or maybe they just didn't need to invent it. Livio hedges his bets, unsatisfyingly arguing that mathematics is partly discovered and partly invented. But Livio is a smooth writer. His fans will enjoy this book, and new ones may discover him. B&w illus. (Jan. 6)Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.
In his latest work, astrophysicist Livio (The Equation That Can't Be Solved; The Accelerating Universe) addresses the puzzle raised by physicist E.P. Wigner and others: How can one account for the "unreasonable effectiveness of mathematics" in the physical sciences? How is it that physicists studying phenomena in such fields as gravity or electricity and magnetism have been able to package all the data into equations that can predict experiments and observations with astonishing accuracy? Among related issues is the question of whether mathematics was invented by humans or whether mathematics is a preexisting structure that was gradually discovered by humans. Livio explores such puzzling ideas by leading readers through the intertwined history of mathematics, science, and logic. He provides apt quotations and helpful explanations within an enjoyable narrative. This is a good popularization of some decidedly nontrivial questions. Recommended for public and academic libraries.
—Jack W. Weigel
Something like that happened to me once, and after I got past my disappointment I found a related subject to research. For Lightman, the incident drove him into another field entirely. Scientists, he decided, were all looking for what was already out there, and the best that he could ever do as a physicist would be to discover something before other scientists did, something that was bound to be discovered eventually anyway. In fiction, Lightman reasoned, he could create something utterly individual, a work that no one else would ever be able to create. Thus began Lightman's award-winning career as a novelist.
But Lightman's certainty that the secrets of the world are sitting out there waiting to be discovered turns out not to be a settled notion at all. What if our discoveries instead turned out to be our own creative -- and inalterably human -- inventions? That is the question that lies at the center of Mario Livio's interesting book Is God a Mathematician?
Livio's title is something of a misnomer, since he barely talks about religion (and then only when discussing the persecution of Galileo) and even less about God. Instead, Livio starts with the observation that thinkers throughout history have made some amazing discoveries about how the world works, and that mathematics is the medium -- the language, he suggests -- in which they have worked. But is math a universal concept or a human invention?
Consider the example of numbers themselves. One mathematician argues that if four dinosaurs stand together in a prehistoric clearing, they number four even though no people are there to count them. In other words, numbers exist independent of human beings. But consider the counterexample (suggested by British mathematician Sir Michael Atiyah) that starts with the imaginary idea that intelligence resides not in people but in a "vast solitary and isolated jellyfish, buried deep in the depths of the Pacific Ocean" with "no experience of individual objects, only with the surrounding water." In this thought experiment, argues Atiyah, "there would be nothing to count." It follows from this second example that numbers -- and all math -- arise from the way that humans perceive the world.
Who's right? That's Livio's focus here. The question is mainly philosophical, but this book is mainly historical. That is, Livio traces the question of discovery versus invention by surveying the most fundamental and influential efforts in the Western tradition to understand the world mathematically. Is God a Mathematician? is a work of intellectual history -- the history of philosophy, logic, and especially math.
Livio talks about math with gratifying clarity, and in a way that doesn't require advanced training to understand it -- but that doesn't mean that it always goes down like chocolate pudding. Some of the concepts Livio introduces, such as the Golden Ratio (the subject of a previous book of his), do require the recollection of some of your high school math. But for the most part, Livio provides not only clear but also strikingly simple explanations, and he backs them up with lively everyday examples. His chapter entitled "Beyond Death and Taxes" showcases one of the more lucid explanations of basic probability theory that I've seen. (The chapter on statistics is likewise valuable, but its necessity to the larger argument is less clear.)
Livio's story of math in the world starts in ancient Greece, with Pythagoras and his followers and their search for "cosmic order" in numbers and ratios. They were the first Platonists, says Livio -- which is to say that they believed that numbers describe a world whose order exists apart from humans, who are privileged to be able to discover that order. From there he blazes through Archimedes, skips forward more than 1,000 years to Galileo, and then slows down. A chapter on Descartes describes beautifully how the Frenchman's work enabled the "systematic mathematicization of nearly everything." In other words, Descartes created ways for the language of mathematics to encompass more and more of the world around us. Livio describes the geometry developed by Descartes with the wonderful example of a subway map.
Isaac Newton was among those who took advantage of Descartes's insights to devise formulas that accounted for, among other things, the workings of gravity. The work of Galileo, Newton, and Descartes, says Livio, created a nearly complete "fusion" between mathematics and scientific exploration. These thinkers believed that math could discover the world.
Then geometry thickened the plot. Euclidean geometry (the kind we learned in high school) works beautifully on its own terms. But not content to stop there, 19th-century mathematicians created other kinds of geometry that worked beautifully on their own terms, even if those terms are for us almost entirely theoretical. The development of non-Euclidean geometry raised the question of whether all geometry -- and with it all math -- might simply be a human construct.
From there it's been back and forth, with math cross-pollinating with logic in the collective effort to settle whether truth exists inside or outside the effort to express it (whether in mathematics or ordinary language). The last part of Livio's story gives a broad outline of the way that the argument between invention and discovery has grown both more heated and more complicated in the past 200 years or so. Finally, he weighs in himself on the question that occupies his book. His brief effort to split the difference between invention and discovery is, well, a bit wishy-washy. But it's no disgrace to be less trenchant than Isaac Newton or Bertrand Russell.
A mathematician I know offers another approach. He says that mathematics should be considered part of the humanities. After all, he argues, math has its own aesthetics, its own elegance, and its own examples of beauty. Maybe so, but it usually requires an advanced degree to see those virtues. Is God a Mathematician? makes some of the beauty of math visible to the layperson -- invented or discovered, no matter. --Leonard Cassuto
Leonard Cassuto is a professor of English at Fordham University and the author of Hard-Boiled Sentimentality: The Secret History of American Crime Stories, now available from Columbia University Press. He can be found on the web at www.lcassuto.com.


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I am very happy with these beautiful throw pillows. I bought 4 20-inch pillows to go on my queen size bed and I wish I had purchased 18-inch pillows because I don't have any place to put them at night. I looked at storage chests but most will only hold 18-incch pillows, if that. Other than that, I really love them.
Welcome! I am a Nature Photographer from Tampa, Florida with an affinity for birds, insects, flowers and trees. My portfolio reflects my love for traveling and includes landscapes from across the United States, Western Europe, China and Japan. Choose from over 6,000 images on a variety of home decor products, including pillows, shower curtains and duvets. All artwork is now available in standard print sizes, such as 8x10, 11x14, 16x20 and 24x36. To find these sizes, click on Wall Art and choose from horizontal, vertical or square. (Watermark will not appear on the final product.)
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subset: commoncrawl


text:
Friday, January 18, 2013
Associated Press
ALGIERS, Algeria
Algerian helicopters and special forces stormed a gas plant in the stony plains of the Sahara on Thursday to wipe out Islamist militants and free hostages from at least 10 countries. Bloody chaos ensued, leaving the fate of the fighters and many of the captives uncertain.
Dueling claims from the military and the militants muddied the world's understanding of an event that angered Western leaders, raised world oil prices and complicated the international military operation in neighboring Mali.
At least six people, and perhaps many more, were killed — Britons, Filipinos and Algerians. Terrorized hostages from Ireland and Norway trickled out of the Ain Amenas plant, families urging them never to return.
Dozens more remained unaccounted for: Americans, Britons, French, Norwegians, Romanians, Malaysians, Japanese, Algerians and the fighters themselves.
The U.S. government sent an unmanned surveillance drone to the BP- operated site, near the border with Libya and 800 miles from the Algerian capital, but it could do little more than watch Thursday's intervention. Algeria's army-dominated government, hardened by decades of fighting Islamist militants, shrugged aside foreign offers of help and drove ahead alone.
With the hostage drama entering its second day Thursday, Algerian security forces moved in, first with helicopter fire and then special forces, according to diplomats, a website close to the militants and an Algerian security official. The government said it was forced to intervene because the militants were being stubborn and wanted to flee with the hostages.
The militants — led by a Mali-based al-Qaida offshoot known as the Masked Brigade — suffered losses in Thursday's military assault but succeeded in garnering a global audience.
Even violence-scarred Algerians were stunned by the brazen hostage-taking Wednesday, the biggest in northern Africa in years and the first to include Americans as targets. Mass fighting in the 1990s had largely spared the lucrative oil-and-gas industry that gives Algeria its economic independence and regional weight.
The hostage-taking raised questions about security for sites run by multinationals that are dotted across Africa's largest country. It also raised the prospect of similar attacks on other countries allied against the extremist warlords and drug traffickers who rule a vast patch of desert across several countries in northwest Africa. Even the heavy-handed Algerian response may not deter groups looking for martyrdom and attention.
Casualty figures in the Algerian standoff varied widely. The remote location is extremely hard to reach and was surrounded by Algerian security forces — who, like the militants, are inclined to advertise their successes and minimize their failures.
"An important number of hostages were freed, and an important number of terrorists were eliminated, and we regret the few dead and wounded," Algeria's communications minister, Mohand Said Oubelaid, told national media, adding that the "terrorists are multinational," coming from several different countries with the goal of "destabilizing Algeria, embroiling it in the Mali conflict and damaging its natural-gas infrastructure."
The official news agency said four hostages were killed in Thursday's operation, two Britons and two Filipinos. Two others, a Briton and an Algerian, died Wednesday in an ambush on a bus ferrying foreign workers to an airport. Citing hospital officials, the APS news agency said six Algerians and seven foreigners were injured.
APS said some 600 local workers were safely freed in the raid — but many of those reportedly were released the day before by the militants themselves.
The militants, via a Mauritanian news website, claimed that 35 hostages and 15 militants died in the helicopter strafing. A spokesman for the Masked Brigade told the Nouakchott Information Agency in Mauritania that only seven hostages survived.
By nightfall, Algeria's government said the raid was over. But the whereabouts of the rest of the plant workers was unclear.
President Barack Obama and British Prime Minister David Cameron spoke on the phone to share their confusion. White House Press Secretary Jay Carney said the Obama administration was "seeking clarity from the government of Algeria."


text:
I do think Mary Quant is a super cute make up range – they're great for eyeshadows, polishes and lipsticks. I bought one of their polishes when I was last at their store – just one because they're £7 and quite small for the price.I got a snotty acid green which has glitter infused in it. Unlike most of the other polishes, this does NOT have a matching lipstick. Shame.
This is a sheer polish – with 2 coats you can make out the green, I wouldn't do less than 2 cos then you will just look like you have dirty nails.
The glitter is micro-multi sparkle and looks lovely:
When it's on it's quite a cute polish although I don't know what you're quite trying to say when you wear a sheer green glittery polish? I'm a weirdo? Yeah, probably.
What do you think of this?


text:
I'm in that seashell Impala with a pelvic scholar
That can spot a fake handbag and smell a dollar
This my love letter, dear jealous cowards
I'm all the way turnt up like Elvis collar
Drop that f*cking top and paint that Lincoln navy blue
Diamond bezel face, my band all white like Blink 182
But don't blink, I maybe view, I might be gone, you might just miss it
Because zero gravity is fly but that's just basic physics
Settle down shawty, hope she ain't your down shawty
How she give the kid some play, it's like she play in house party
How they gon' outsmart me? They need better schooling
I gave your girlfriend the dope di*k and left her drooling
My jeweler called me, asked me will I give him 30
To put black ice in my piece, Will.I.Am and Fergie
They say will I give 'em mercy, Why? n*ggas can't reverse my fire
Hungry sun, thirsty sky, I'm starving and the earth is pie
Stare you in your worthless eyes, penetrate your shallow soul
Plus I got some f*cking swag, that'll make your shadow cold
They don't want me in battle mode, my sh*t more like war mode
Smack your f*cking face and stomp the organs out your torso
Then I'm on my tours, yo, f*ck these hoes, get more dough
Till everything in my house Italian, no Jersey Shore show
They can't go where your boy go, got an asteroid flow
Been nice from the get go, and I ain't talking Geico
Squirrel, I'm powered up, fresh to death and showered up
Jump on that hooligan express, scoop your homie out the cut
And they know we out that what where they swing them techs and AK's
That'll smash ya homie, you know, Danger, Precious, Ray J
Lames just better play safe, they frightened from the f*cking truth
Hit these n*ggas in the head like a sniper on the roof
Uh, I give 'em cold stares, no grin
See my target, hold my breath, then I zero in


text:
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Jeep Commander Water Leak and Radio Problem
swift1776 Posts: 1Hi bwilliams,
I too have a 2006 Commander Hemi; I purchased it new. My car first stalled on the highway after two years; my gauge said I had a quarter tank left. However, the sending unit malfunctioned and I was on empty. Fixed under warranty. Then the Trans Over Temp warning kept coming on. For several months the Temp light would come on at random and the car would stall; sometimes at low speeds, sometimes on the highway doing 60MPH! The dealership replaced the sensor and it still came on and still stalled. Then they hardwired the Temp sensor to the ECU. Still came on. Then a Trans specialist at the dealer looked at it; the transmission was actually overheating; the Trans pump was failing causing the care to Trans to overheat and make the car stall. They dropped the transmission, rebuilt it and it stalls no more. However, the car intermittently does not start. This they cannot figure out.
The new issue, which was discovered a few months ago was the exhaust manifolds are warped and both have broken bolts. New forged manifolds won't be in until Sept 24, 2012. They know there is a problem with this so I we get yours checked. The excessive heat in the engine compartment has caused the paint to peel on the hood. It appears as bubbles and when you touch them the paint falls off revealing a white powder.0
tjzeke Posts: 1I took the Jeep into the dealer after having gone to Speedy Auto Glass because of the front floor board flooding on the driver's side. I thought they did a faulty installation of my windshield. But this had been almost a year ago. The technician said problems usually show up immediately. He did a test and the windshield was fine. He was nice enough to help me out and found a clogged drain tube by the sunroof. He even cleaned it out which wasn't that easy. He ran water on that side of the car and Viola, no more leak.
But the next time it rained I discovered a flooded floor board on the passenger side. I took the '06 Commander Limited to the dealer and he got it fixed.
I told him I was very skeptical because of all the complaints I had read on the internet and wanted to know if the dealership guaranteed the work. He said yes and then took me into the parking lot and ran lots of water all over the sunroof. No leaks.
I asked him to tell me what he did. I told him I wanted to post it on the internet. It has been about 3 months ago that he did the fix and there have been at least 6 or 7 rain storms since then and no signs of leaking. So I am finally posting what he told me as his fix worked for me.
He said this leakage problem occurs when the sunroof is not totally in line with the roof. If the sunroof is either too high or too low it compresses the gasket either too little or too much leading to leaks. To correct the problem first you need to place the sunroof in the "vent" position. Then look for 2 (two) allen screws on both the right and left sides of the sunroof. On my Jeep they are silver in color and easy to see against all the other black trim and rubber. Loosen the screws and make the necessary adjustments. He said this might take several attempts to get the sunroof perfectly in line with the rest of the roof.
I hope this is an easy fix. It sounds simple enough but then I didn't have to do it. Good luck.0
tomison Posts: 1Lets not toss the baby out with the bath water! In this case, rain water.
The "blue tube" issue is a piece of cake, and if anyone charged you $250 to blow it out, they ripped you off! It doesn't even require any tools! The problem isn't the tube, but the grommet in the floor the tube plugs into. It is crimped at the end and gets plugged up from debris from the road. The water can't drain and overflows the catch pan of the sunroof, into your roof liner, down the b-pillars to the dash and floor pan.
Just pull the door kick plate(snapped on by clips) then pull the side molding from the under dash foot area, by pulling from the front toward the back. Held on by two clips as well. This will reveal the "blue tube". Lift up carpet to see black rubber grommet the tube goes into. It's soft rubber, so pull tube out of grommet, and then the grommet out of floor pan. The end of the grommet is crimped and exposed to the undercarriage, so it needs to be cleaned off. Then, just blow into the tube ( or use air compressor), to move any debris out. Open sunroof and clean out any leaves or dirt out of the pan and away from the drain holes in the front corners of the sunroof pan.
Took less than 15min. Poor design but easy fix.
Also may want to peel the tape from the drain holes in the bottom of the doors. Mine were also collecting water. Hope it helps!0
yeabuddy89 Posts: 1I had the same problem with my 06 with 65k miles. The sunroof was an easy fix after pulling back the carpet and cleaning out the sunroof drain tubes. The transmission light it another story... The light would come on intermittenly and would turn off automatically or after a restart. Took it to the dealer 2 times where it remained the first time for a few days and the second time for 4 weeks. They could not get it to replicate this and told me everything appeared to be operating normally and gave me the runaround that it may be the solenoid pack(replaced less than 1 year prior at the same dealership)or the computer or some bypass valve. I called jeep corporate to inform them of the issue with the dealership and vehicle and they were of no help. so I pulled it out of service. Overall, I was very dissatisfied with the dealer for not even offering a refund for the diagnostic fee which they could not dianose and for jeep corporate with there lack of assitance. Really makes me hesitant to own another jeep product as i have been a loyal owner since driving nothing but jeeps for 11 years. Thanks jeep. your awesome and really know to keep your customers coming back. Not!0
1moparman Posts: 1So after going back to dealer what has happened? we have an 06 commander also and believe this should be something that was disclosed when purchasing vehicle which we bought new have had this problem before, dealer took care of it but now vehicle is out of warranty and now 6 to 7 yrs later they tell us that it needs regular maintenance for this problem. So for yours, ours and everyone out there with this problem I am going to call0
thisisrich Posts: 1I have an '06 Commander that I've had since new. For the first time yesterday I had water leaking out both A-pillars and a distinct sloshing sound on turns. Shortly after that the radio started cutting in and out and the speedo and tach started moving erratically. Assorted dash warning light coming on and off completed the picture.
I have never had leaks before but based on all of these posts it's clear I am not alone. Now the radio comes on but there is no sound at all.
Had generally had a good experience other than horrendous gas mileage and a windshield that seems to be a magnet for every pebble out there.
Will check the drain tubes but I fear the radio is toast. There should be a recall for this.0
Isn't a shame that there has been no recall. I guess you will have to join all of us Commander owners who cannot leave our garages when it rains. And when we have to, we always have a tarp come along w/us..... Something should be done! Shame on you Jeep!!!0
alloyfinder Posts: 2I have an '07 Commander Ltd Hemi that has been leaking for over a year. Thought initially it was a faulty install of a new windshield. Windshield company ran water tests and told me the leak was coming from eroded fasteners on floorboard.
Carpets are molded.
Recently, the front windows do not open and the radio does not shut off when I turn off the car.
I have 1 more month on the lease, and I am dreading turn in.0
justbe77 Posts: 1This was the solution to the leaking sunroof issue that you are experiencing. It was due to a design flaw of the draining tubes. This YouTube video shows how to remedy the problem.
We just purchased a 2007 Commander Overland and have the same problem now with the radio not shutting off when I turn off the jeep and the next day my front windows won't open. Has anybody figured out what this problem is with the 2007? I'm waiting now for other things to go wrong, I sure hope not, as I'm sure repairs aren't very cheap. Thanks for any help on this.0
What the big problem is that it's not repairs are expensive, but rather no one has a clue why these cars are having all these problems so they cannot fix the problems. So you are basically throwing your money out every time you bring the car in for a repair...no one can actually fix the problems. It's just disgusting how the company did not have a recall on these vehicles. I wonder how many of us drive around with a tarp in our cars. The only ones that don't have a problem are those who cover their cars when it rains. So go buy a tarp and throw it over the car when it rains and you will have better luck than bringing it to a dealer. Good Luck...I cannot even talk about it anymore...it makes me sick!!0
Actually, i had some of those problems on my 2006 jeep commander and going through this blog, i found some tips to fix some of the issues so I would recommend you to keep digging this blog to find solutions.
i would recommend you to lift carpet and sub insulation on both driver and passenger front floor and look for leaks.
The issue is most of the wiring is going on the floor for all front dash commands and seats and if it is in the water, then you start to have some of the issues like radio not working, heater not functioning properly, etc...
one of the fix I found is the blue pipe (drain) going vertically from dashboard to floor along the main structure of the car. this is the drain of the sun roof and this pipe is cut too short, so, instead of pouring the excess of water outside from the hole on the floor, it pours inside and fill up your car with water.
the fix is easy ; go to home depot or Lowes and buy a clear flexible tube just on size up of the blue pipe so you can insert the blue pipe onto it tightly and drive this pipe through the hole in the floor and long enough so you can see/feel it under your car from outside.
but before you do that, try to blow air onto the blue pipe in case it may be clogged.
the reason i am using a clear pipe is that you can see in the future if there is clogging or material going through this pipe, which means it is time to clean it
This would get rid of flooding on the front of your jeep.
I believe there is the same drain issue towards the center and the back of the car but i did not explore that part yet... i am waiting for better weather so i can work outside on the car without freezing myself.
One thing is : don t change the joint of your door or the seal of your windshield or any of the BS the jeep dealer wants to sell you because it will not fix the problem and they know it
Keep the faith, we will overcome this, together, as a team ; we can be stronger than a corporation0
Thanks for the tip on the blue tube ; it helped me figured out that my blue tube was cut too short and was pouring inside the car instead of outside ; I extended it and worked like a charm ; I don t have a swimming pool in the passenger side anymore.
I still have leaks in the rest of the car, lost the lighting on the dashboard for the heater and ventilation, the radio button can only be controlled on the wheel but i keep hope to fix things as we go and explore...
At the end, i think i will be able to un-build and rebuild this car my eyes closed lol0
it is a great car and fall in love as soon as i sat in the driver seat but I agree, i would never bought it if i knew all the major water and electrical problems we have with those cars ; it is just unsafe and would not recommend you to buy one.
each time i drive, i expect something to go wrong and always watch out for something to go terribly wrong
not a fun way to drive0
did you check the blue pipe - do a search for blue pipe or blue tube on this blog and you ll have your solution for the water leak on the passenger side
this is the drain of the sunroof that is clogged or cut too short and pour into your car instead of outside.
rip off the carpet and insulation from the floor, look at the frame on top right and you ll see a blue tube going down vertically to the floor and normally onto a hole on the floor and outside
first, blor air into it to see if it is clogged, then pour water on your sunroof to make sure water goes through it and then extend it and make sure the tube goes through the floor
that will fix your problem0
We just took our 2007 commander into the dealer because of the radio not working and the front windows not rolling down, just like yours. It was a pinched wire going to the sunvisor, so you might want to check it out on your vehicle. Everything is working again since they unpinched it. Just thought this might be your problem.0
07commander206 Posts: 1Hello,
place me on your list of folks to contact mine started leaking last year.0
itabot Posts: 105I agree, maybe a thread titled just 'Jeep Commander Class Action' should be initiated, then let that on-line presence build and see if an attorney doesn't pick it up then?
I just received the safety recall notice re. commander that reflects problems people within the Edmunds Forum have been complaining about since 2006.
The problem they say could be corrected by software fix but Jeep can't get in touch with the software manufactuer so they are replacing - if I have it right - the transfer case actuator.
As someone else had said the source of most of these commander problems were 1. the software and 2. poor quality components at time of initial manufacturing. (everything that has been replaced in my Commander - it's basically a rebuild) has not caused any problems.0
marty91 Posts: 1If you do get an attorney,please let me know. I have a 2006 Jeep commander and leaks badly and my handles are broken this is the worst pue I have ever bought. It just looks good.0
kimmyb1 Posts: 1My 2006 Comander leaks like crazy, I went out one day after a good rain and there were 3 inches of water in the drivers side floor. Lights are shorting out and it got so bad we drilled a small hole so the water could drain. We thought it was coming from the back sun windows and sealed those but it still is leaking. You can hear the water move from the top of the door when you are turning the corner. Now the transmission is hot light is coming on.. We already had to have a differential put in just a month a go. The car has 65 thousand miles on it.. I dont get it0
jeepercreep Posts: 1I own a 2006 Limited 5.7 HEMI and had the same leaking problem. I followed the fix instructions in the YouTube video above () and it worked beautifully. NO MORE LEAKING!! Of course since I've already been swimming around inside my Jeep for the last year or so, my radio/nav screen just has lines across it (like a bar code) rendering the NAV useless. I was told by the Jeep dealer that I could do a swap out for $975. For that price I can get a better aftermarket radio/nav with bluetooth, wifi, HDD, etc. However, since this is an expense that could have been prevented by the manufacturer widening the grommet hole at the bottom of the sunroof drain tube, I feel that I should be reimbursed for my expenses. My carpets also are beginning to mold, so that is going to be a future expense. Oh, and to list my problems so far: radiator cracked and replaced, cylinder misfires, rough idle, broken sunroof, replaced cyl 5/7 lifter bank, cylinder 7 MDS solenoid replaced, pushrods-intake valve replaced, 4WD front and rear harnesses and actuator axle locker replaced. I bought the Jeep in April 2012 and as of today has 85K miles on it. (It began leaking around July/August 2012 at 65K-70K miles.)0
robinclong Posts: 1I have a 2006 jeep commander the sunroof is leaking and now my u connect stopped working and also my door handles on the inside are broken. I have also had an incident where the right front ball joint broke when I was driving wont he road and my car slid across the road on the tire with it laying on the rim. Had we been going faster than 25mph we probably would not be here . I ended up costing me 1700 to fix and now to have this sunroof and blue tooth ( uconnect) issue it's driving me nuts. My ac is also making a noise when I turn it on now like something's in the fan... Any advice would be great ...I have the 2006 limited jeep commander with 5.7 hemi around 80,000 miles0
nickisloan Posts: 1I read several messages. I have a leak as well with my passenger side filling with water with a big rain. I love my car, just want it fixed, and now my radio does not work. If anyone has contacted a lawyer please let me know. Will get the blue tubes checked.0
anticommander Posts: 1I wish I had read these messages prior to buying my 2008 Jeep Commander. It's like I have a swimming pool on the drivers side after it rains really hard. I have not heard of any recalls but I am certainly trying to find one. The smell in the car after it rains is horrible. That in itself is a health hazard. I cannot believe that Jeep would make a product that is so defective. Who wants to drive with a small puddle under their feet? Certainly not I. When I took it back to the dealership they told me that they don't think the shortage in the radio is connected with the water leaking but I refuse to believe that. This is really annoying. I will NEVER buy another Jeep Commander in my life.0
thegalwaygirl Posts: 1I have less than 100,000 miles on my 2006 jeep commander. The heating and cooling system has always been a problem. A week ago the blower stopped working and I am so fed up with constantly having it looked at and temporarily fixed that I was going to tough it out but of course the defogger does not work so I took it back today. Unable to diagnose or fix the problem the mechanic suggested that I contact Chrysler to see if there were any recalls due to this particular problem and that is how I found this site. I had water problems that were addressed by the dealership while it was under warranty and water problems after the warranty expired. I have had water on both the passenger and driver side. There has to be rust issues and mold issues as well. It was so bad, I kept the wet vac in the back of the jeep After I vacuumed, I then used 3 to 4 beach towels to soak up most of the remaining water. If I were in a position to donate the car, my conscience would cry! Has anyone had any problems with the heating or cooling system or with the blower? Thanks.0
wswig Posts: 14I have the exact same problems. I have been on this site for several years. We all have the same complaints. I have small leakage at the top of my windshield which is a safety problem. I haven't had a radio for years. I lost my blower a couple of months ago. I may have to get the blower fixed. We have to get everyone that has complaints to contact one party that may help us get these problems resolved. Good luck to you and hope we can get some support somewhere.0
banner4g Posts: 1
We also have a 2006 Jeep Commander with water leaking issues. But we do NOT have a sunroof. Have owned the vehicle for many years without problems, but now the passenger side foot well fills with water after a hard rain. It reeks of mold/mildew. The smell is almost unbearable. Even if we miraculously fix the leaking, I don't know that we will ever get rid of the stench.
I saw the video posted above for Commanders with a sunroof. Wondering if there is a similar hack for fixing the leak on Commanders without a sunroof.0
foxxygranny57 Posts: 1I have the same problem as all of you. I have a 2006 commander, purchased in 2008. I just started having trouble this year, 2014. When it rain really hard I have a lot of water on the floor on the driver side of truck. I was told it was the windshield, so I took it to replace the windshield, but they put the truck in a pressure washer to see exactly where the water was coming from, it wasn't the windshield. Please help now I have no idea where the h2o is coming in from.. If there is a lawsuit out there anywhere about this issue,, please. Someone let the rest of us know. Thanks0
treester Posts: 1We have a 2007 Jeep Commander. Suffering with the wet floors also for years and no radio. We did the sun roof drain cleaning and trim the nipples like everyone else. Also did the door gasket secondary seal tbs suggested. It still leaked. Radio still turned on but no sound..... The amp is out....where is the amp.... Found it.... Back left hand panel( no where near front drain tubes)... And has water damage. We took almost the whole inside apart to find the leak. Here is what we figured out. Our problem resides with the roof rack. The top body frame is like a gutter and that's why you may hear sloshing sound. The front 2 bolts are rusted and noticed all the bolts are not tightly seal and secured. We silicone the heck out of each bolt and the rivets that the bolts screw into it. We are now looking for a replacement amp. hopes this helps any commander owner.0
olugo3552 Posts: 1Hi guys. My 2007 commander it doesn't have sunroof and I have it since 2008. Around 2010 I founded water right in the middle of the dash. It is coming from the rear little mirow inside and after that it was occasionally leaking water depended how it was parked. Now it is leaking water from the right arm handle from the screw too. If any one of you commander owners know what is going on or how I can fix this please let me know. My email is [email protected]0


text:
You are awesome. :D I'm a large, and a blue with white ink would be great, but otherwise a green with white ink. Thanks so much!
I'm in two minds about his appearance. Whilst I admit to very much liking his company, I fear that his presence in and around my house is causing a few of the birds to become nervous and worried, particularly the sparrows that live in a large bush near to the top of my garden. I would rather the birds feel at home than the cat, if I am speaking honestly. The cat has another home, the birds don't know another home, particularly the younger souls. I trust that Amelia and Abraham are well, and that their young have learnt safely to fly.
Well over one month since you last shared news with me of Amelia and Abraham, I am back. I'm afraid that I haven't ever read 'The Crows of Pearblossom' by Huxley, only 'Brave New World'. Speaking of crows, over the past two months, we've had consistent visits from Jackdaws in the Garden - I've always called them Hooded Crows, I don't know if that's the correct name for them, but I've picked it up from somewhere. A few weeks ago I counted 15 of the creatures sitting in the dead tree at the bottom of my garden at dusk, it was a positively eerie sight. Lately a cat has been frequenting my home as well; he appears every day around two o' clock and places a paw on the patio doors, waiting to be let inside. He often wanders every room in the house, occasionally taking the time to fall asleep on the stairs, then precedes to go back to whichever place he calls his home.
I'm sorry I didn't say so sooner, but the photograph you shared with me was beautiful. The doves look like such kindly creatures. Have you assigned each of them names? My father occasionally makes bird houses for the garden, and this year we have Robin's living in one of them. I would attach a photograph, but they are terribly timid animals, and I cannot get close enough to photograph them to an adequate standard, so you'll have to make do with this artist's (photographers) impression; I hope it suffices. [IMG]http://cr7.e2bn.net/e2bn/leas/c99/schools/cr7/homepage/Robin%20Class/section0-tvl-backto-X2Fe2bnX2FleasX2Fc99X2FschoolsX2Fcr7X2FhomepageX2F-media-1-quizX5Fid-z20090112174427173X2Dw001X2DX54X50X2DX50rocessor248X2D108918-u-20090112174427173X2Dw001X2DX54X50X2DX50rocessor248X2D108918-z-f.jpeg[/IMG]
it's a friday... June 10th. BUT you could come and just not go back to Maine and change your name and we can kick my cousin who I can't stand out or we could get bunk beds and stuff.
maybe we should both skip popfest (I'm suffering from the same delusions as you) and go to the Andrew Bird show. OR YOU COULD COME SEE HIM FREE IN NYC WITH ME AND TACKLEDSPOON and anyone else who comes :'D
or we could do all of the above.
Senior E6er
Junior E6er


text:
Smoking After Diagnosis of Breast Cancer
Dear OncoLink "Ask The Experts,"
Can you please provide more information on the subject of smoking while receiving chemotherapy and radiation treatment for breast cancer?
What is the effect of continued smoking while receiving treatment, due to cigarette smoke containing over 4000 chemical compounds, hundreds of which are either poisonous or carcinogenic?
When must a patient diagnosed with breast cancer stop smoking?
Carolyn Vachani RN, MSN, AOCN, OncoLink's Nurse Educator, responds:
First off, smoking is never a good thing. We always hope to prevent people from ever starting, let alone needing to quit. Although smoking is not associated with the diagnosis of breast cancer, there is ample evidence that patients who smoke do not tolerate chemotherapy and radiation therapy as well as nonsmokers. Fortunately, we know improvements in the bodies' ability to function begin within 24 hours of a patient quitting smoking.
In some cancers (such as lung), studies have suggested that outcomes are better for those who quit smoking at diagnosis. People who quit smoking often feel that they have more energy almost immediately, which could certainly be a benefit when chemotherapy-induced fatigue sets in. Smoking can irritate mouth sores (a common side effect of chemotherapy) or affect the ability to taste, which can make eating even more difficult while on therapy - both good reasons to quit.
When radiation is delivered for breast cancer, part of the lung receives radiation which can affect a small amount of its function. Those who smoke have less reserve then nonsmokers and this could potentially impact their overall lung function down the road. More importantly left sided breast irradiation does treat some of the heart and has been shown to increase the risk of coronary artery disease. Smoking greatly increases the risk of developing coronary artery disease and potentially puts the patient at even greater risk of heart problems down the road.
Quitting smoking is not easy, but fortunately there are options for assistance including medications and behavioral modification techniques. It is important for smokers to discuss this with their physicians so appropriate strategies can be developed to help them quit the habit and stay off the cancer sticks.


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|Home > Florida Then & Now > Opinion/Proof Strategy
Opinion/Proof Notes
This strategy helps students learn to develop an opinion, and support it through evidence from a text.
The students read an assigned chapter or book.
The students develop an opinion about a character from the text. The opinion is written down in the left-hand column.
- The students write supporting evidence for their opinion in the right-hand column. The evidence must be derived from the text along with the page number for reference.
- The students share their opinion/proof notes with the class. Extension: The students may use their opinion/proof notes to develop a persuasive paper.
Santa, C. (1993). Pegasus: Teacher implementation guide for grade 4. Dubuque, Iowa: Kendall/Hunt Publishing Company.
|Home > Florida Then & Now > Opinion/Proof Strategy
Florida: A Social Studies Resource for Students and Teachers
Produced by the Florida Center for Instructional Technology,
College of Education, University of South Florida © 2002.


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$ 105.00
Arrowhead plant a.k.a. Nephthytis is easy to grow and comes in a wide variety of different colors and leaf patterns. When the plant matures it develops a climbing habit and will look great on a window or shelf. If you decide not to let it climb, the plant can be easy pruned and kept in an upright shape.
Leaf color WILL VARY depending on availability.
Benefit: Air Purifier.
Botanical Name: Syngonium Podophyllum
Light: Low to medium. No direct sun.
Planter: Built in sub-irrigation system - water your plant 3 times less often in comparison to regular pots. Wick self-watering system. Made by Lechuza in Germany, shatterproof, highest quality,100% recyclable plastic. High-gloss finish.
Planter size: 11.8"L x 4.3W x 5.1"H
Approx. height of potted plant: 10"
Sending plant as a gift? You will be able to add your gift message at the checkout.
Note: Shape, color and height of plants will vary.
For now we deliver plants to Manhattan, Brooklyn, Bronx, Queens, Staten Island, Jersey City, Edgewater and Hoboken.
We offer the Next Day delivery for orders placed before 11 am but recommend placing larger orders few days in advance to assure availability.
Rarely, requested delivery date needs to be changed due to stock availability or temporary weather conditions. In this case, we will contact you to re-schedule the delivery.
Delivery hours:
Monday: 12 pm - 6 pm
Tuesday - Friday: 7 am - 6 pm
Saturday: 9 am - 3 pm
Note: Orders for Monday delivery should be placed by 11 am on Friday. We do not deliver on Sundays.
Delivery Fee Per Entire Order
Long Island City - $14.95
Manhattan, Rest of Queens, Brooklyn – $19.95
Bronx, Jersey City, Edgewater & Hoboken – $39.95
Staten Island - $44.95
|Light Intensity
|Bright Light
|South or southwest-facing windows. Direct sunlight.
|Medium Light
|East or West facing windows. Partial, filtered or indirect sunlight.
|Low Light
|North-facing windows. No more then 20 feet from the window. Bright fluorescent light at least 8-10 hours a day.
Note: if you can't read a book as it is too dark in a certain areas than it is too dark for any plant as well.
Window direction is not the only factor to understand your light situation. What is outside the window makes a big difference. Another building, large tree, etc. will block direct light and will effect lighting environment.
Want to learn more about light? Read our Light Guide.


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Annual attendance at the 2013 Black Hat security conference has increased significantly in recent years. This year, more than 7,500 were in attendance, according to conference organizers.
The hacking conference has been known for research that showcases high-profile attacks targeting hardware and software vulnerabilities. With attendance at its highest, there was a heightened need for security vendors to gain security professionals' attention on the expo floor. The following security firms appeared to be getting the lion's share of attention for the roles they play in network monitoring, malware detection and analysis capabilities.


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NASHVILLE, Tenn. – First-year Lipscomb women's soccer coach Kevin O'Brien got a chance to see his team in a game situation Friday evening in the exhibition version of the "Battle of the Boulevard."
Long-time Rival Belmont scored a late goal to take a 2-1 victory at Rose Park.
After a scoreless first half the Lady Bisons got on the scoreboard first as Baylee Linnell broke free from the defense and scooted a goal under the attacking Bruins goalkeeper Nicole Berner, just 58 seconds into the second half.
The Bruins struck just two minutes later when Taylor Smith found the back of the net with an assist from Sydney Scheben.
In the 72nd minute, LU had an opportunity to score as Caroline Chadwell hit a well-struck ball that Berner made a save on, preventing the Bisons lead.
In the 85th minute, LU goalkeeper Erin Zerio put a phenomenal diving save on Lauren Paynter's shot. On the ensuing corner kick, the Bruins connected with a header from Laura Harris to take the 2-1 lead and the victory.
LU took seven shots, placing five on goal. Chadwell had five shots with Linnel and Karli Crosby each taking one apiece.
The Lady Bisons will open regular season play on Friday Aug. 17 as they play host to Jackson State in a 7 p.m. affair at the Lipscomb Soccer Complex.


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Major Section: PROGRAMMING
(Mv-nth n l) is the
nth element of
l, zero-based. If
n is
greater than or equal to the length of
l, then
mv-nth returns
(Mv-nth n l) has a guard that
n is a non-negative integer and
l is a
Mv-nth is equivalent to the Common Lisp function
nth, but is used by
ACL2 to access the nth value returned by a multiply valued expression. For
an example of the use of
mv-nth, try
ACL2 !>:trans1 (mv-let (erp val state) (read-object ch state) (value (list erp val)))


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GOES Soundings Vertical Profile JAVA Loops
North American Cities and Adjacent Coastal Waters
NESDIS Office of Research and Applications
on interpretation of atmospheric temperature and moisture soundings derived from GOES satellite data.
Station List
of GOES Soundings
Latest GOES Soundings Locations Plotted Over Infrared Satellite Cloud Image.
Click on location (designated by three - five digit
on map below to display GOES satellite derived temperature and moisture sounding.
NOTE: GOES satellite soundings are available only when sky conditions are clear or partly cloudy.
In cloudy conditions, or when GOES sounder data is missing, a message 'Sounding Unavailable' will be displayed.
As such, you may need to deselect certain images in the requested JAVA animation.
Your browser does not support script
For more information please contact
Hank Drahos, Chief, FPDT,
to GOES Soundings
Last Updated 06/08/2005


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Newt's route: Leave no state behind
For Newt Gingrich, who announced his candidacy Wednesday, the road to the Republican nomination runs through Iowa.
And New Hampshire, South Carolina, Nevada and Florida.
Story Continued Below
Unlike some of his likely rivals, who are looking to downplay or even flat out skip some states on the primary calendar, Gingrich is headed down a different path, a more traditional route in which he will compete aggressively across the early-state map and among all blocs within the party.
That most likely means participating in this summer's Iowa GOP straw poll in Ames, traditional retail politicking in New Hampshire and making an all-out effort in South Carolina. But Gingrich officials say their effort will be bigger than any one state and look dramatically different than any other campaign.
Since Mitt Romney and Jon Huntsman can spend their own millions on their campaigns and remain on the airwaves even after sustaining early losses, advisers to the former House speaker don't believe it's possible to lock up the nomination by winning one or even two initial contests. So Gingrich isn't pinning his hopes on any single state, believing instead that, for those who can't fund their own campaigns, the drawn-out contest will require a prudent use of resources spread across the board. (See also: Jon Huntsman to storm New Hampshire)
"You've got to compete everywhere and appeal to Republican primary voters across the board — you can't cherry-pick places [where] you think you can win," said Dave Carney, a New Hampshire-based Gingrich strategist and longtime GOP consultant, predicting a "long, hard-fought battle," thanks to the prospective self-funders.
"Even if their ideas aren't working and they're not getting any traction, they can stay in the race," he said.
Said another Gingrich adviser: "Newt's a national candidate. He has a national brand. He's a national leader."
The former speaker already is gearing up in first-in-the-nation Iowa. In addition to directing $150,000 last year to a campaign that unseated a trio of state Supreme Court justices who had ruled unconstitutional a state ban on same-sex marriage, Gingrich is putting together a strong field organization and is expected to show up at Ames.
"I certainly think so," said state Rep. Linda Upmeyer, a leader of Gingrich's Iowa effort, when asked whether he'll participate in the straw poll. "When it comes to how you are going to get out there and fill the [news] vacuum, you want to be part of that news that might fill that vacuum." (See also: Bob Vander Plaats: Iowa is do or die for Mike Huckabee)
In Iowa, Gingrich has almost precisely the opposite problem as Tim Pawlenty, who is also working hard there. Both are lagging in early-state polls, but the former Minnesota governor's status can be mostly chalked up to his lack of name identification among GOP activists. Gingrich, however, faces what may ultimately be a more daunting task. He enjoys almost universal recognition among primary voters but must convince them that he's not just the '90s-era-leader-turned-Fox-News-commentator but also a potential president in 2012.
"He's been to Iowa several times — but never actually campaigning," said J. Ann Selzer, who conducts the respected Iowa Poll. "He's seen as the think guy, the ponderous professor. He's not acting in the presidential candidate role — just yet."
"He's probably past his presidential shelf life," said Andrew Smith, a professor and pollster at the University of New Hampshire. "You usually win the presidency within 10 to 12 years of being in office."


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Gov. Rick Perry, who told a San Antonio audience that he'll focus on Texas for the next 18 months while he serves out his last term, told the Washington Times that he's headed to Israel in October
From the Washington Times story, bannered as an exclusive:
"We will be going to Israel to bring together Arabs, Christian and Jews in an educational forum," Mr. Perry told The Washington Times in an interview just three days after he announced he would not seek an unprecedented fourth term as Texas governor.
Many analysts interpreted that decision as evidence that he is setting the table for a White House campaign. Asked what would induce him to announce a run, he told The Times that he has "plenty of time to make that decision."
When Perry announced at Holt Cat in San Antonio Monday that he wouldn't seek re-election, he said:
"I am looking forward to the next 18 months as I serve out my term. Any future considerations I will announce in due time, and I will arrive at that decision appropriately. But my focus will remain on Texas."
Perry spokeswoman Lucy Nashed declined to confirm Perry's trip or his itinerary:
"As always, we will notify the media about details of any travel at the appropriate time."


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By: Kevin Hale Back to Guides
Alright, everyone! Today is the last day for you to play our Mad iPad Giveaway contest and get registered to win a tricked out iPad. For those of you that have already played (thanks!), I thought I'd take some time to share how we created the fun Mad Lib part using the various features in Wufoo. The Mad Lib form uses a number of our features and showcases just how versatile Wufoo's system is for designing really creative data collection experiences.
Pick a Story
This is probably the most difficult part about creating a Mad Lib form. Like most things that are funny, you have to have a good handle on the punchline. In a Mad Lib, that means revealing a funny story that's the result of unexpected words showing up in a fairly simple story. If you're looking for some inspiration, there's a great set of ideas that can be found over at It's a Mad Libs World!. The inspiration for our Mad Lib in the contest came out of an excerpt I saw from a press release about the iPad:
With the iPad, navigation has never been easier or more intuitive. Because you use the most natural pointing device there is: your finger. All you have to do to scroll through a web page is flick your finger up or down on the screen.
Looking at that sentence, I looked at all the nouns an adjectives and realized that if I replaced some of the words like iPad, web page, finger and screen, that it could be a pretty funny story. With that in hand, I wrote a fake press release for an innovative company coming out with a new revolutionary product and created a list of all the key nouns and adjectives I wanted the user to replace with their own words.
Design the Form
With the list of words I needed from the user, I quickly designed a form in Wufoo asking for those words.
I made all of the fields required (so our story doesn't have any gaps) and I also asked for an email address on the first page of the form so that I could email a copy of the completed story to the user as a keepsake.
If you want to run a contest like ours, you might want to make it so you check off the No Duplicates validation for the email address field so that only one unique entry can be submitted at a time and also use our Form Scheduling feature to set the start and end dates for when the form is active and collecting entries.
The feature that makes the Mad Lib form just work is Wufoo's Templating system. It allows you to take the data sent by the user and send it back to them on a confirmation page, inside a confirmation email and even in a payment receipt and invoice.
To use templating in Wufoo, you'll first have to get a list of the API Field IDs associated with each field. You can find this information in the Code Manager. It'll contain a list of your forms along with a table containing the fields and their IDs. Using that info and our Templating documentation, you can contstruct the templating tags needed to display the data on the confirmation page. For example, if I want to display what the user entered for the Fruit field, I find the field ID for that field, which is 115 and then use that to create the proper template tag, which is {entry:Field115}. That means from the entry for that form display the data for field with an ID of 115. So using that, I mapped the fields and their appropriate tags into the story I wrote earlier like so:
{entry:Field115} Releases New Revolutionary {entry:Field116}
{entry:Field115} today introduced {entry:Field116}, a revolutionary device for browsing {entry:Field123}, enjoying {entry:Field117}, watching {entry:Field119}, playing {entry:Field120}, reading {entry:Field122}, and much more.
The {entry:Field126} Multi-Touch screen on {entry:Field116} lets you see {entry:Field125} as they were meant to be seen — one {entry:Field124} at a time.
With {entry:Field116}, navigation has never been easier or more intuitive. Because you use the most natural pointing device there is: your {entry:Field127}. All you have to do to scroll through a {entry:Field124} is flick your {entry:Field127} up or down on the screen.
At just {entry:Field134} inches thick and {entry:Field135} pounds, {entry:Field116} is thinner and lighter than any {entry:Field128}.
Unlike {entry:Field139}, which is {entry:Field130} for {entry:Field131} people, {entry:Field116} is {entry:Field136} done right.
Please note that I also wrapped each template tag in some bold tags so I can use that style them differently and pop them out on the confirmation page using CSS. I can then use that text and insert them in text I want to show on the Confirmation page. Because I also wanted to let the user get a copy of the entry when they left, I also set up the confirmation email to use the same templated info.
Custom CSS
If you want to make your Mad Lib story a little more fancy and emphasize the words that were entered by the user, you can stylize those bold tags around the template tags with some custom styles. In Wufoo, you can use our Theme Designer to attach your own CSS style rules in an external stylesheet. I uploaded a CSS file to Amazon S3 called contest.css with the following CSS rule to highlight those tags.
.confirm b{
border-bottom:2px solid #ccc;
Now, when the user submits the form, the confirmation page will underline and highlight the users' words like so:
You can learn more about using your own CSS Stylesheet in our documentation on custom CSS.
Once you're all done, you can even create a report that will show the most popular answers for each word you asked for the Mad Lib. Here's a link to our report for the Mad Lib contest.
And that's it! The form doesn't take very long to create and our users seem to be getting a kick out of making their own revolutionary product announcements. Please give it a try and enjoy making your own Mad Libs!