Computational Beauty Of Nature Quotes

To all the secret writers, late-night painters, would-be singers, lapsed and scared artists of every stripe, dig out your paintbrush, or your flute, or your dancing shoes. Pull out your camera or your computer or your pottery wheel. Today, tonight, after the kids are in bed or when your homework is done, or instead of one more video game or magazine, create something, anything. Pick up a needle and thread, and stitch together something particular and honest and beautiful, because we need it. I need it. Thank you, and keep going.

A society where feminine beauty is defined not by the human self on genuine intellectual and sentimental grounds, but by a computer software on the grounds of economic interest, is more dead than alive. It is a society of human bodies, not human beings.

In general, we look for a new law by the following process: First we guess it; then we compute the consequences of the guess to see what would be implied if this law that we guessed is right; then we compare the result of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works. If it disagrees with experiment, it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is, it does not make any difference how smart you are, who made the guess, or what his name is — if it disagrees with experiment, it is wrong.

Nature—the sublime, the harsh, and the beautiful—offers something that the street or gated community or computer game cannot.

There is a most profound and beautiful question associated with the observed coupling constant, e - the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!

As the physicist Richard Feynman once observed, “[Quantum mechanics] describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So I hope you can accept nature as She is— absurd.” Quantum mechanics seems to study that which doesn’t exist—but nevertheless proves true. It works. In the decades to come, quantum physics would open the door to a host of practical inventions that now define the digital age, including the modern personal computer, nuclear power, genetic engineering, and laser technology (from which we get such consumer products as the CD player and the bar-code reader commonly used in supermarkets). If the youthful Oppenheimer loved quantum mechanics for the sheer beauty of its abstractions, it was nevertheless a theory that would soon spawn a revolution in how human beings relate to the world.

If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.

Most people have all the time in the world. They’ll live to be eighty or older. But they don’t use the time they have. They waste it on the couch, in front of the TV, or at the computer. They don’t have time for the things that make life really worth living: other people, their friends and family, the friendship of a dog, the beauty of nature… They’ve lost all mindfulness.

Printers are like that,’ I say. ‘It’s in their nature. They print when you don’t need anything. And when you really need something printed out, the ink cartridge is empty or there’s a sheet of paper jammed inside, the printer tells you it’s lost its internet connection or that it doesn’t recognise the computer you’re trying to print from. If you ask me, the whole idea of a digital, paperless future is down to the fact that printers have driven so many people to despair and insanity. Paper is a good thing; it’s beautiful. There’s nothing wrong with paper: it feels pleasant in your hand and it’s the best way to read something. The only problem is getting those little black marks onto the surface of the paper in the first place. Even with all the modern technology at our disposal it’s all but impossible. I suspect – no, I’m absolutely convinced – that the printer companies and the antidepressant manufacturers of this world are in cahoots.

By virtue of this filling of the causal gap, the most important demand of intuition – namely that one's conscious efforts have the capacity to affect one's own bodily actions – is beautifully met by the quantum ontology. And in this age of computers, and information, and flashing pixels there is nothing counterintuitive about the ontological idea that nature is built – not out of ponderous classically conceived matter but – out of events, and out of informational waves and signals that create tendencies for these events to occur.

I think we're all just doing our best to survive the inevitable pain and suffering that walks alongside us through life. Long ago, it was wild animals and deadly poxes and harsh terrain. I learned about it playing The Oregon Trail on an old IBM in my computer class in the fourth grade. The nature of the trail has changed, but we keep trekking along. We trek through the death of a sibling, a child, a parent, a partner, a spouse; the failed marriage, the crippling debt, the necessary abortion, the paralyzing infertility, the permanent disability, the job you can't seem to land; the assault, the robbery, the break-in, the accident, the flood, the fire; the sickness, the anxiety, the depression, the loneliness, the betrayal, the disappointment, and the heartbreak. There are these moments in life where you change instantly. In one moment, you're the way you were, and in the next, you're someone else. Like becoming a parent: you're adding, of course, instead of subtracting, as it is when someone dies, and the tone of the occasion is obviously different, but the principal is the same. Birth is an inciting incident, a point of no return, that changes one's circumstances forever. The second that beautiful baby onto whom you have projected all your hopes and dreams comes out of your body, you will never again do anything for yourself. It changes you suddenly and entirely. Birth and death are the same in that way.

A Code of Nature must accommodate a mixture of individually different behavioral tendencies. The human race plays a mixed strategy in the game of life. People are not molecules, all alike and behaving differently only because of random interactions. People just differ, dancing to their own personal drummer. The merger of economic game theory with neuroscience promises more precise understanding of those individual differences and how they contribute to the totality of human social interactions. It's understanding those differences, Camerer says, that will make such a break with old schools of economic thought. "A lot of economic theory uses what is called the representative agent model," Camerer told me. In an economy with millions of people, everybody is clearly not going to be completely alike in behavior. Maybe 10 percent will be of some type, 14 percent another type, 6 percent something else. A real mix. "It's often really hard, mathematically, to add all that up," he said. "It's much easier to say that there's one kind of person and there's a million of them. And you can add things up rather easily." So for the sake of computational simplicity, economists would operate as though the world was populated by millions of one generic type of person, using assumptions about how that generic person would behave. "It's not that we don't think people are different—of course they are, but that wasn't the focus of analysis," Camerer said. "It was, well, let's just stick to one type of person. But I think the brain evidence, as well as genetics, is just going to force us to think about individual differences." And in a way, that is a very natural thing for economists to want to do.

simple enjoyment of the beauty and wonder of nature is sometimes called “fascination attention.” It is the opposite of “directed attention,” which we employ when we are actively trying to hold our focus on a specific task or object, like when using the computer, attending meetings, or planning and strategizing.

You are created to be a creator. God does not give anyone a finished product. God did not create the telephone, car, computers, Facebook, amazon, ebay, God did not make a chair, He created a tree for you to produce the chair. He gave you the raw materials to look at and ask yourself what can I do with this? Are you a producer or a consumer? .....ponder

Looking back at the organization of the sciences, we find that at teach level of understanding, traditional scientists study two types of phenomena: agents(molecules, cells, ducks, and species) and interactions of agents (chemical reactions, immune system responses, duck mating, and evolution). Studying agents in isolation is a fruitful way of discovering insights into the form and function of an agent, but doing so has some known limitations. Specifically, reductionism fails when we try to use it in a reverse direction. As we shall see throughout this book, having a complete and perfect understanding of how an agent behaves in no way guarantees that you will be able to predict how this single event will behave for all time or in the context of other agents.

Now, take all of your computer's memory and arrange it as one long line of zeros and ones: 0,1,1,1,0,0,0,1,1,0,1....Take this very long number and put a zero and a decimal point in front of it. We've just translated one huge number into a rational number between 0 and 1. By placing this single point at exactly the right spot on the number line, we can store an unlimited amount of information. Ah, if only it were so simple. In the real world, we simply don't have the precision required to put this method of storing memory into practice. We never will, either, but it's an interesting mental exercise to see that it can be done in theory in an idealized world. The point of this whole mental exercise is that in many ways an irrational number has as much "information" as an infinite number of natural numbers.

Later Turing proved that Turing machines could compute exactly the same functions as lambda calculus, which proved that all three models of computation are equivalent. This is a truly remarkable result, considering how different the three models of computation are. In Church's 1941 paper he made a statement that is now known as the Church-Turing thesis: Any function that can be called computable can be computed by lambda calculus, a Turing machine, or a general recursive function. Recall the point that was made about functions describing relationships between numbers and models of computation describing functions. Well, the Church-Turing thesis is yet another level more fundamental than a model of computation. As a statement about models of computation, it is not subject to proof in the usual sense; thus, it is impossible to prove that the thesis is correct. Once could disprove it by coming up with a model of computation over discrete elements that could calculate things that one of the other models could not; however, this has not happened. The fact that every posed model of computation has always been exactly equivalent to (or weaker than) one of the others lends strong support to the Church-Turing thesis.

We have, then, three different ways of looking at how things work. We can take a purely reductionist approach and attempt to understand things through dissection. We also can take a wider view and attempt to understand whole collections at once by observing how many agents, say the neurons in a brain, form a global pattern, such as human intelligence. Or we can take an intermediate view and focus attention on the interactions of agents. Through this middle path, the interactions of agents can be seen to form the glue that binds one level of understanding to the next level.

Any discrete piece of information can be represented by a set of numbers. Systems that compute can represent powerful mappings from one set of numbers to another. Moreover, any program on any computer is equivalent to a number mapping. These mappings can be thought of as statements about the properties of numbers; hence, there is a close connection between computer programs and mathematical proofs. But there are more possible mappings than possible programs; thus, there are some things that simply cannot be computed. The actual process of computing can be defined in terms of a very small number of primitive operations, with recursion and/or iteration comprising the most fundamental pieces of a computing device. Computing devices can also make statements about other computing devices. This leads to a fundamental paradox that ultimately exposes the limitations not just of machine logic, but all of nature as well.

Moreover, multiplicity, iteration, and adaptation are universal concepts in that they are apparently important attributes for agents at all levels-from chemical reactants to biological ecosystems.

The goal of this book is to highlight the computational beauty found in nature's programs.

Soon after that, Eno briefly joined a group called the Scratch Orchestra, led by the late British avant-garde composer Cornelius Cardew. There was one Cardew piece that would be a formative experience for Eno—a piece known as “Paragraph 7,” part of a larger Cardew masterwork called The Great Learning. Explaining “Paragraph 7” could easily take up a book of its own. “Paragraph 7”’s score is designed to be performed by a group of singers, and it can be done by anyone, trained or untrained. The words are from a text by Confucius, broken up into 24 short chunks, each of which has a number. There are only a few simple rules. The number tells the singer how many times to repeat that chunk of text; an additional number tells each singer how many times to repeat it loudly or softly. Each singer chooses a note with which to sing each chunk—any note—with the caveats to not hit the same note twice in a row, and to try to match notes with a note sung by someone else in the group. Each note is held “for the length of a breath,” and each singer goes through the text at his own pace. Despite the seeming vagueness of the score’s few instructions, the piece sounds very similar—and very beautiful—each time it is performed. It starts out in discord, but rapidly and predictably resolves into a tranquil pool of sound. “Paragraph 7,” and 1960s tape loop pieces like Steve Reich’s “It’s Gonna Rain,” sparked Eno’s fascination with music that wasn’t obsessively organized from the start, but instead grew and mutated in intriguing ways from a limited set of initial constraints. “Paragraph 7” also reinforced Eno’s interest in music compositions that seemed to have the capacity to regulate themselves; the idea of a self-regulating system was at the very heart of cybernetics. Another appealing facet of “Paragraph 7” for Eno was that it was both process and product—an elegant and endlessly beguiling process that yielded a lush, calming result. Some of Cage’s pieces, and other process-driven pieces by other avant-gardists, embraced process to the point of extreme fetishism, and the resulting product could be jarring or painful to listen to. “Paragraph 7,” meanwhile, was easier on the ears—a shimmering cloud of sonics. In an essay titled “Generating and Organizing Variety in the Arts,” published in Studio International in 1976, a 28-year-old Eno connected his interest in “Paragraph 7” to his interest in cybernetics. He attempted to analyze how the design of the score’s few instructions naturally reduced the “variety” of possible inputs, leading to a remarkably consistent output. In the essay, Eno also wrote about algorithms—a cutting-edge concept for an electronic-music composer to be writing about, in an era when typewriters, not computers, were still en vogue. (In 1976, on the other side of the Atlantic, Steve Jobs and Steve Wozniak were busy building a primitive personal computer in a garage that they called the Apple I.) Eno also talked about the related concept of a “heuristic,” using managerial-cybernetics champion Stafford Beer’s definition. “To use Beer’s example: If you wish to tell someone how to reach the top of a mountain that is shrouded in mist, the heuristic ‘keep going up’ will get him there,” Eno wrote. Eno connected Beer’s concept of a “heuristic” to music. Brecht’s Fluxus scores, for instance, could be described as heuristics.

Our present intricate humanly consciousness evolved after a long journey of struggle. And the beauty of natural selection is that our struggle against nature made us worthy of being rewarded with the 3 lbs. lump of highly advanced biological computer by our Mother Nature herself.

I highly recommend a crystal salt lamp in the room to help to balance the ions and improve the electro-magnetic balance of the air. The benefits of these naturally beautiful lamps are well known. While most ionizers on the market are just so many more man-made machines, the salt crystal lamp is a beautiful alternative of Mother Nature, without any noise and no harmful ozone added to our homes. Salt crystal lamps are highly beneficial for daily use in the whole house. Bed rooms, living rooms, dining rooms, and especially near televisions, computers and around smokers, to neutralize the damage being put out from those sources. Use these lovely lamps to reduce your own fatigue, a crystal salt lamp near your child’s computer will minimize the ill effect of all that radiation and bring a soothing effect to the surroundings of your child’s work area; they improve concentration and refresh the child naturally by neutralizing the effects of an artificial environment. Please place a small crystal salt light in your child’s

When I asked a Portuguese mathematician of my acquaintance whether he had any insight to offer me on the subject, he replied, “The foundations of mathematics are full of holes and I never felt comfortable dealing with such things.” Full of holes. Earlier generations of mathematicians assumed that the stability of the landscape on which mathematical structures were built was guaranteed by God or nature. They strode in like pioneers or surveyors, their task to map the fundamentals and in so doing secure the territory that future generations would colonize. But then the holes—of which the liar’s paradox is merely one—started popping up, and the mathematicians started falling in. Never mind! Each hole could be plugged. But soon enough another would open, and another, and another . . . Bertrand Russell (1872–1970) spoke for any number of idealistic mathematicians when he wrote in 1907, The discovery that all mathematics follows inevitably from a small collection of fundamental laws, is one which immeasurably enhances the intellectual beauty of the whole: to those who have been oppressed by the fragmentary and incomplete nature of most existing chains of deduction, this discovery comes with all the overwhelming force of a revelation: like a palace emerging from the autumn mist as the traveller ascends an Italian hill-side, the stately storeys of the mathematical edifice appear in their due order and proportion, with a new perfection in every part. I remember that when I read George Eliot’s Middlemarch in college, I was particularly fascinated by the character of Mr. Casaubon, whose lifework was a Key to All Mythologies that he could never finish. If Mr. Casaubon’s Key was doomed to incompletion, my astute professor observed, it was at least in part because “totalizing projects,” by their very nature, ramify endlessly; they cannot hope to harness the multitude of tiny details demanded by words like “all,” just as they cannot hope to articulate every generalization to which their premises (in this case, the idea that all mythologies have a single key) give rise. Perhaps without realizing it, my professor was making a mathematical statement—she was asserting the existence of both the infinite and the infinitesimal—and her objections to Mr. Casaubon’s Key hold as well for any number of attempts on the part of mathematicians to establish a Key to All Mathematics.

Now that I was living closer to nature, I realized that this was the real world, very different from the man-made world of automobiles, computers and skyscrapers. Man was a god of sorts in his own sphere, but on a lovely mountainside he is no more important than an ant—and not half as industrious!