Probability Distribution Quotes

I’ve come to believe that genius is an exceedingly common human quality, probably natural to most of us. I didn’t want to accept that notion — far from it: my own training in two elite universities taught me that intelligence and talent distributed themselves economically over a bell curve and that human destiny, because of those mathematical, seemingly irrefutable scientific facts, was as rigorously determined as John Calvin contended.

A category of government activity which, today, not only requires the closest scrutiny, but which also poses a grave danger to our continued freedom, is the activity NOT within the proper sphere of government. No one has the authority to grant such powers, as welfare programs, schemes for re-distributing the wealth, and activities which coerce people into acting in accordance with a prescribed code of social planning. There is one simple test. Do I as an individual have a right to use force upon my neighbor to accomplish this goal? If I do have such a right, then I may delegate that power to my government to exercise on my behalf. If I do not have that right as an individual, then I cannot delegate it to government, and I cannot ask my government to perform the act for me…In reply to the argument that a little bit of socialism is good so long as it doesn't go too far, it is tempting to say that, in like fashion, just a little bit of theft or a little bit of cancer is all right, too! History proves that the growth of the welfare state is difficult to check before it comes to its full flower of dictatorship. But let us hope that this time around, the trend can be reversed. If not then we will see the inevitability of complete socialism, probably within our lifetime.

Yes, genes explain far more about us than anyone had realized, but the genes themselves often turn out to be sensitive to environmental conditions. And yes, each person has a characteristic level of happiness, but it now looks as though it's not so much a set point as a potential range or probability distribution.

Bayes’s theorem and that looks like this: People who understand Bayes’s theorem can use it to work out complex problems involving probability distributions—or inverse probabilities, as they are sometimes called.

A probabilistic mind-set pertaining to trading consists of five fundamental truths. 1. Anything can happen. 2. You don’t need to know what is going to happen next in order to make money. 3. There is a random distribution between wins and losses for any given set of variables that define an edge. 4. An edge is nothing more than an indication of a higher probability of one thing happening over another. 5. Every moment in the market is unique.

Probably no country has ever had as large a shift in the distribution of wealth [as what we've seen in the U.S. in the last 30 years] without having gone through a revolution or losing a major war.

I believe that you have the absolute right to think things that I find offensive, stupid, preposterous or dangerous, and that you have the right to speak, write, or distribute these things, and that I do not have the right to kill you, maim you, hurt you, or take away your liberty or property because I find your ideas threatening or insulting or downright disgusting. You probably think some of my ideas are pretty vile too. I

The wide-ranging birds that visit islands of the ocean in migration may also have a good deal to do with the distribution of plants, and perhaps even of some insects and minute land shells. From a ball of mud taken from a bird's plumage, Charles Darwin raised 82 separate plants, belonging to 5 distinct species! Many plant seeds have hooks or prickles, ideal for attachment to feathers. Such birds as the Pacific golden plover, which annually flies from the mainland of Alaska to the Hawaiian Islands and even beyond, probably figure in many riddles of plant distribution.

So let’s talk a little about April May’s theory of tiered fame. Tier 1: Popularity You are a big deal in your high school or neighborhood. You have a peculiar vehicle that people around town recognize, you are a pastor at a medium-to-large church, you were once the star of the high school football team. Tier 2: Notoriety You are recognized and/or well-known within certain circles. Maybe you’re a preeminent lepidopterist whom all the other lepidopterists idolize. Or you could be the mayor or meteorologist in a medium-sized city. You might be one of the 1.1 million living people who has a Wikipedia page. Tier 3: Working-Class Fame A lot of people know who you are and they are distributed around the world. There’s a good chance that a stranger will approach you to say hi at the grocery store. You are a professional sports player, musician, author, actor, television host, or internet personality. You might still have to hustle to make a living, but your fame is your job. You’ll probably trend on Twitter if you die. Tier 4: True Fame You get recognized by fans enough that it is a legitimate burden. People take pictures of you without your permission, and no one would scoff if you called yourself a celebrity. When you start dating someone, you wouldn’t be surprised to read about it in magazines. You are a performer, politician, host, or actor whom the majority of people in your country would recognize. Your humanity is so degraded that people are legitimately surprised when they find out that you’re “just like them” because, sometimes, you buy food. You never have to worry about money again, but you do need a gate with an intercom on your driveway. Tier 5: Divinity You are known by every person in your world, and you are such a big deal that they no longer consider you a person. Your story is much larger than can be contained within any human lifetime, and your memory will continue long after your earthly form wastes away. You are a founding father of a nation, a creator of a religion, an emperor, or an idea. You are not currently alive.

A red dragonfly hovers above a backwater of the stream, its wings moving so fast that the eye sees not wings in movement but a probability distribution of where the wings might be, like electron orbitals: a quantum-mechanical effect that maybe explains why the insect can apparently teleport from one place to another, disappearing from one point and reappearing a couple of meters away, without seeming to pass through the space in between. There sure is a lot of bright stuff in the jungle. Randy figures that, in the natural world, anything that is colored so brightly must be some kind of serious evolutionary badass.

So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand.[...]Even though many economic and financial variables fall into distributions that approximate a bell curve, the picture is never perfect.[...]It is in those outliers and imperfections that the wildness lurks.

The normal distribution describes the manner in which many phenomena vary around a central value that represents their most probable outcome;

You have a very high probability of your quote and your name being distributed, posted, and shared around the world!

Since the dawn of time, several billion human (or humanlike) beings have lived, each contributing a little genetic variability to the total human stock. Out of this vast number, the whole of our understanding of human prehistory is based on the remains, often exceedingly fragmentary, of perhaps five thousand individuals. You could fit it all into the back of a pickup truck if you didn't mind how much you jumbled everything up, Ian Tattersall, the bearded and friendly curator of anthropology at the American Museum of Natural History in New York, replied when I asked him the size of the total world archive of hominid and early human bones. The shortage wouldn't be so bad if the bones were distributed evenly through time and space, but of course they are not. They appear randomly, often in the most tantalizing fashion. Homo erectus walked the Earth for well over a million years and inhabited territory from the Atlantic edge of Europe to the Pacific side of China, yet if you brought back to life every Homo erectus individual whose existence we can vouch for, they wouldn't fill a school bus. Homo habilis consists of even less: just two partial skeletons and a number of isolated limb bones. Something as short-lived as our own civilization would almost certainly not be known from the fossil record at all. In Europe, Tattersall offers by way of illustration, you've got hominid skulls in Georgia dated to about 1.7 million years ago, but then you have a gap of almost a million years before the next remains turn up in Spain, right on the other side of the continent, and then you've got another 300,000-year gap before you get a Homo heidelbergensis in Germany and none of them looks terribly much like any of the others. He smiled. It's from these kinds of fragmentary pieces that you're trying to work out the histories of entire species. It's quite a tall order. We really have very little idea of the relationships between many ancient species which led to us and which were evolutionary dead ends. Some probably don't deserve to be regarded as separate species at all.

Entropy theory is indeed a first attempt to deal with global form; but it has not been dealing with structure. All it says is that a large sum of elements may have properties not found in a smaller sample of them. Entropy theory, on the other hand, is not concerned with the probability of succession in a series of items but with the overall distribution of kinds of items in a given arrangement.

In mathematical physics, quantum field theory and statistical mechanics are characterized by the probability distribution of exp(−βH(x)) where H(x) is a Hamiltonian function. It is well known in [12] that physical problems are determined by the algebraic structure of H(x). Statistical learning theory can be understood as mathematical physics where the Hamiltonian is a random process defined by the log likelihood ratio function.

The Incas’ genius— like that of the Romans—lay in their masterful organizational abilities. Amazingly, an ethnic group that probably never exceeded 100,000 individuals was able to regulate the activities of roughly ten million people. This was in spite of the fact that the empire’s citizens spoke more than seven hundred local languages and were distributed among 2,500 miles of some of the most rugged and diverse terrain on earth.

Total circulation will be 21,000,000 coins. It’ll be distributed to network nodes when they make blocks, with the amount cut in half every 4 years. first 4 years: 10,500,000 coins next 4 years: 5,250,000 coins next 4 years: 2,625,000 coins next 4 years: 1,312,500 coins etc... When that runs out, the system can support transaction fees if needed. It’s based on open market competition, and there will probably always be nodes willing to process transactions for free.

No behavior has an infinite set of possibilities. Think of a lightning strike, although the state space is very high the bolt never make as a u-turn. The idea of infinities came from Feynman's thought experiment involving the twin slit measurement having an infinite number of slits. The probability distribution is not infinite, there are ratios involved. If reality contains both infinity and unity, it is either a multifaceted jewel, or the singularity dancing. The fiddler is self referential noise.

It would probably be best if managers went to the IT department and asked that e-mail not be distributed between eight and eleven every morning. The idea that the best way to communicate with people is 24/7 is not really an idea about maximizing productivity.

Mine is a parish like all the rest.  They’re all alike.  Those of to-day I mean.  I was saying so only yesterday to M. le Curé de Norenfontes—that good and evil are probably evenly distributed, but on such a low plane, very low Indeed! Or if you like they lie one over the other; like oil and water they never mix.  M. le Curé only laughed at me.

1. Anything can happen. 2. You don’t need to know what is going to happen next in order to make money. 3. There is a random distribution between wins and losses for any given set of variables that define an edge. 4. An edge is nothing more than an indication of a higher probability of one thing happening over another. 5. Every moment in the market is unique.

If you have programmers, they probably save their code in Git, which is the closest I can think of to a useful blockchain-like technology: it saves individual code edits as transactions in Merkle trees with tamper-evident hashes, and developers routinely copy entire Git repositories around, identifying them by hash. It’s a distributed ledger, but for computer programs rather than money.

In statistical mechanics, in other words, we think that there actually is some particular classical state of all the particles, but we don’t know it, all we have is a distribution of probabilities. Happily, such a distribution is all we need to do a great deal of useful physics, since it fixes properties such as the temperature and pressure of the system. But the distribution isn’t a complete description of the system; it’s simply a reflection of what we know (or don’t) about it. To tag this distinction with philosophical buzzwords, in statistical mechanics the probability distribution is an epistemic notion—describing the state of our knowledge—rather than an ontological one—describing some objective feature of reality. Epistemology is the study of knowledge; ontology is the study of what is real.

According to our estimates, the optimal top tax rate in the developed countries is probably above 80 percent.50 Do not be misled by the apparent precision of this estimate: no mathematical formula or econometric estimate can tell us exactly what tax rate ought to be applied to what level of income. Only collective deliberation and democratic experimentation can do that. What is certain, however, is that our estimates pertain to extremely high levels of income, those observed in the top 1 percent or 0.5 percent of the income hierarchy. The evidence suggests that a rate on the order of 80 percent on incomes over $500,000 or $1 million a year not only would not reduce the growth of the US economy but would in fact distribute the fruits of growth more widely while imposing reasonable limits on economically useless (or even harmful) behavior.

This brings me to the question of the antiquity of the belief in fairies and to the associated problem of the existence of strata or stages in fairy belief. The antiquity of the belief is revealed by the wide distribution of tales concerning fairies, while it is also indicated by the antipathy of the elves to iron and salt - ancient taboos both. Not only so, but many traits respecting fairies, especially shape-shifting and the belief in their semi-corporeal state, are eloquent of primitive notions. That the process of the fairy belief witnessed more than one stage of development in the course of successive ages appears more than probable. 'The fairies of one race,' remarks Wentz, 'are the people of the preceding race.' If this statement lacks a certain precision, one realizes the implication; that is, that the ghosts or gods of a preceding race may come to be regarded by their successors as fairies.

The great thing about talent is it's the one thing, the only thing I can think of, that is absolutely randomly distributed throughout the population of the world. It has nothing to do with anything. You cannot buy it. You cannot learn it, you cannot inherit it. [...] And [this] is probably the reason why so many people, especially in this country, are looking for explanations for success of a book--and when I say success, I mean commercial success--other than talent. Because it's infuriating to people.

The wave quality of light is the same as that of the electron. The wave determines the probable location of the photon of light when it is detected. The wave character of light is not vibrating stuff like a wave of water but rather a wavelike function encoding information about where you'll find the photon of light once it is detected. Until it reaches the detector plate, like the electron, it is seemingly passing through both slits simultaneously, making its mind up about its location only once it is observed [...]. It's this act of observation that is such a strange feature of quantum physics. Until I ask the detector to pick up where the electron is, the particle should be thought of as probabilistically distributed over space, with a probability described by a mathematical function that has wavelike characteristics. The effect of the two slits on this mathematical wave function alters it in such a way that the electron is forbidden from being located at some points on the detector plate. But when the particle is observed, the die is cast, probabilities disappear, and the particle must decide on a location.

For every one member of the elite, thousands more were illiterate and impoverished subsistence farmers. After the ‘collapse of civilisation’, many of them moved elsewhere, and some may have died, but for the most part their lives probably did not change much. They went on growing crops. Those people were your ancestors and mine—not the palace-dwellers, but the peasants. Our rich and complex international networks of production and distribution have come to an end before, but here we are, you and I, and here is humanity. What if the meaning of life on earth is not eternal progress toward some unspecified goal—the engineering and production of more and more powerful technologies, the development of more and more complex and abstruse cultural forms? What if these things just rise and recede naturally, like tides, while the meaning of life remains the same always—just to live and be with other people?

Modern statistics is built on the idea of models — probability models in particular. [...] The standard approach to any new problem is to identify the sources of variation, to describe those sources by probability distributions and then to use the model thus created to estimate, predict or test hypotheses about the undetermined parts of that model. […] A statistical model involves the identification of those elements of our problem which are subject to uncontrolled variation and a specification of that variation in terms of probability distributions. Therein lies the strength of the statistical approach and the source of many misunderstandings. Paradoxically, misunderstandings arise both from the lack of an adequate model and from over reliance on a model. […] At one level is the failure to recognise that there are many aspects of a model which cannot be tested empirically. At a higher level is the failure is to recognise that any model is, necessarily, an assumption in itself. The model is not the real world itself but a representation of that world as perceived by ourselves. This point is emphasised when, as may easily happen, two or more models make exactly the same predictions about the data. Even worse, two models may make predictions which are so close that no data we are ever likely to have can ever distinguish between them. […] All model-dependant inference is necessarily conditional on the model. This stricture needs, especially, to be borne in mind when using Bayesian methods. Such methods are totally model-dependent and thus all are vulnerable to this criticism. The problem can apparently be circumvented, of course, by embedding the model in a larger model in which any uncertainties are, themselves, expressed in probability distributions. However, in doing this we are embarking on a potentially infinite regress which quickly gets lost in a fog of uncertainty.

Buffett was asked why he hadn't bought more Costco shares, considering that Munger owns shares and is on the board of directors. "Yeah, you hit on a good one here," Buffett replied. "We should've owned more Costco, and probably if Charlie had been sitting in Omaha, we would've owned more Costco. Charlie was constantly telling me about this terrific method of distribution, and after 10 years or so I started catching on to what he was saying, and we bought a little of Costco at Berkshire. "We actually negotiated to buy more. I made the most common mistake that I make . . . We started buying it, and the price went up, and instead of following it up and continuing to buy more. . . . If Costco had stayed at $15 a share or so, where we were buying it, we would've bought a lot more. But instead it went to 15⅛ and who could pay 15⅛ when they'd been paying $15—it wasn't quite that bad. But I have made that mistake a lot of times, and it's very irritating."23

The overwhelming consensus is that egalitarian social organization is the de-facto system for foraging societies in all environments. In fact, no other system could work for foraging societies. Compulsory sharing is simply the best way to distribute risk to everyone’s benefit: participation mandatory. Pragmatic? Yes. Noble? Hardly. We believe this sharing behavior extended to sex as well. A great deal of research from primatology, anthropology, anatomy, and psychology points to the same fundamental conclusion: human beings and our hominid ancestors have spent almost all of the past few million years or so in small, intimate bands in which most adults had several sexual relationships at any given time. This approach to sexuality probably persisted until the rise of agriculture and private property no more than ten thousand years ago. In addition to voluminous scientific evidence, many explorers, missionaries, and anthropologists support this view, having penned accounts rich with tales of orgiastic rituals, unflinching mate sharing, and an open sexuality unencumbered by guilt or shame.

Look,” she told me one day in a Millsport coffeehouse. “Shopping—actual, physical shopping—could have been phased out centuries ago if they’d wanted it that way.” “They who?” “People. Society.” She waved a hand impatiently. “Whoever. They had the capacity back then. Mail order, virtual supermarkets, automated debiting systems. It could have been done and it never happened. What does that tell you?” At twenty-two years old, a Marine Corps grunt via the street gangs of Newpest, it told me nothing. Carlyle took in my blank look and sighed. “It tells you that people like shopping. That it satisfies a basic, acquisitive need at a genetic level. Something we inherited from our hunter-gatherer ancestors. Oh, you’ve got automated convenience shopping for basic household items, mechanical food distribution systems for the marginalized poor. But you’ve also got a massive proliferation of commercial hives and speciality markets in food and crafts that people physically have to go to. Now why would they do that, if they didn’t enjoy it?” I probably shrugged, maintaining my youthful cool. “Shopping is physical interaction, exercise of decision-making capacity, sating of the desire to acquire, and an impulse to more acquisition, a scouting urge. It’s so basically fucking human when you think about it. You’ve got to learn to love it, Tak. I mean you can cross the whole archipelago on a hover; you never even need to get wet. But that doesn’t take the basic pleasure out of swimming, does it? Learn to shop well, Tak. Get flexible. Enjoy the uncertainty.

The passion for truth and justice often gives those who experience it a start. Those who experience it? But surely to desire truth and justice is the same thing as to be a man, to be human. However unequally distributed such a passion may be, it marks the extent to which each man is human – to which human dignity is due to him. Marcel Proust wrote in Jean Santeuil: It is always with a joyful and positive emotion that we hear those bold statements made by men of science who, for a mere question of professional honour, come to tell the truth – a truth which only interests them because it is true, and which they have to cherish in their art without hesitating to displease those who see it in a very different light and who regard it as part of a mass of considerations which interest them very little.1 The style and the content of this passage are very different from A la Recherche du temps perdu. Yet, in the same book, the style changes, but not the thought: What moves us so much in Phaedo is that, as we follow Socrates’ arguments, we suddenly have the extraordinary feeling that we are listening to an argument whose purity is unaltered by any personal desire. We feel as if truth were superior to everything, because we realise that the conclusion that Socrates is going to draw is that he must die.2 Marcel Proust wrote about the Dreyfus case around 1900. His dreyfusard sympathies are known to us all, but after A la Recherche du temps perdu, written ten years later, he lost his ingenuous aggressiveness. We ourselves have also lost that simplicity. The same passion may occasionally arouse us, but, on the whole, we are too tired, too indifferent. A Dreyfus case in our day would probably cause little stir …

Another plan, to march on Alexander’s court nearly four hundred miles away in St Petersburg itself, was proposed, but Berthier and Bessières quickly convinced Napoleon on logistical grounds ‘that he had neither time, provisions, roads, nor a single requisite for so extensive an expedition’.32 Instead they discussed marching south nearly 100 miles to Kaluga and Tula, the granary and arsenal of Russia respectively, or retreating to Smolensk. Napoleon eventually chose what turned out to be the worst possible option: to return to the Kremlin, which had survived the fire, on September 18 to wait to see whether Alexander would agree to end the war. ‘I ought not to have stayed in Moscow more than two weeks at the utmost,’ Napoleon said later, ‘but I was deceived from day to day.’33 This was untrue. Alexander didn’t deceive Napoleon into thinking he was interested in peace; he simply refused to reply either positively or negatively. Nor was Napoleon self-deceived; the burning of Moscow confirmed him in his belief that there was no hope of peace, even though he would probably have accepted as little as Russia’s return to the Continental System as the price.34 The reason he stayed in Moscow for so long was that he thought he had plenty of time before he needed to get his army back to winter quarters in Smolensk, and he preferred to live off the enemy’s resources. On September 18, Napoleon distributed 50,000 plundered rubles to Muscovites who had lost their houses and he visited an orphanage, dispelling the widespread rumour that he was going to eat its inhabitants.35 ‘Moscow was a very beautiful city,’ he wrote to Maret, using the past tense. ‘It will take Russia two hundred years to recover from the loss which she has sustained.

The situation gets still more concerning. As Chapter Six argues, two important factors that are frequently assumed to be constants in the traditional security dilemma models are in fact variables in cybersecurity. In most other security dilemma discussions, each actor sees the moves of its potential adversaries and must determine the intentions behind those moves. In cybersecurity, the distribution of information is vastly more asymmetric, which increases risk and uncertainty for decision-makers. With proper tradecraft, many actions, including the development of powerful capabilities and the launching of significant intrusions, often remain out of view to others. Thus, unlike in many historical and theoretical textbook cases, in cyber operations not only must states potentially fear what they see, but they must potentially fear what they do not see as well. Defensive-minded intrusions that resolve this uncertainty thus seem still more appealing. Similarly, in the traditional security dilemma model there is almost always some status quo of shared expectations. This implicit or formal consensus of behavior provides significant guidance about which activities the involved parties consider normal and non-threatening. The potential for escalation in this model occurs only when this shared vision of normalcy breaks. In cybersecurity, however, there is only a nascent status quo. Without a common conception of appropriate national behavior, the probability of dangerous misinterpretation increases. Building on these five steps to the argument, the final two chapters of the book are somewhat different in kind. Chapter Seven pauses to consider three objections to the cybersecurity dilemma logic and how they might constrain the argument.

Wondering if Westcliff was going to reprimand the boys for allowing her and Daisy to play, Lillian said uneasily, “Arthur and the others—it wasn’t their fault—I made them let us into the game—” “I don’t doubt it,” the earl said over her shoulder. “You probably gave them no chance to refuse.” “You’re not going to punish them?” “For playing rounders on their off-time? Hardly.” Removing his coat, Westcliff tossed it to the ground. He turned to the catcher, who was hovering nearby, and said, “Jim, be a good lad and help field a few balls.” “Yes, milord!” The boy ran in a flash to the empty space on the west side of the green beyond the sanctuary posts. “What are you doing?” Lillian asked as Westcliff stood behind her. “I’m correcting your swing,” came his even reply. “Lift the bat, Miss Bowman.” She turned to look at him skeptically, and he smiled, his eyes gleaming with challenge. “This should be interesting,” Lillian muttered. Taking up a batter’s stance, she glanced across the field at Daisy, whose face was flushed and eyes over-bright in the effort to suppress a burst of laughter. “My swing is perfectly fine,” Lillian grumbled, uncomfortably aware of the earl’s body just behind hers. Her eyes widened as she felt his hands slide to her elbows, pushing them into a more compact position. As his husky murmur brushed her ears, her excited nerves seemed to catch fire, and she felt a flush spreading over her face and neck, as well as other body parts that, as far as she knew, there were no names for. “Spread your feet wider,” Westcliff said, “and distribute your weight evenly. Good. Now bring your hands closer to your body. Since the bat is a few inches too long for you, you’ll have to choke up on it—” “I like holding it at the base.” “It’s too long for you,” he insisted, “which is why you pull your swing just before you hit the ball—” “I like a long bat,” Lillian argued, even as he adjusted her hands on the willow handle. “The longer the better, as a matter of fact.” A distant snicker from one of the stable boys caught her attention, and she glanced at him suspiciously before turning to face Westcliff. His face was expressionless, but there was a glitter of laughter in his eyes. “Why is that amusing?” she asked. “I have no idea,” Westcliff said blandly, and turned her toward the pitcher again.

The enemy won some points at the very beginning. On both of the two days preceding his remarks about Worth, Hitchcock notes that American deserters had been shot while crossing the Rio Grande. Probably they were just bored with army rations but there was some thought that they might be responding to a proclamation of General Ampudia’s which spies had been able to circulate in camp. Noting the number of Irish, French, and Polish immigrants in the American force, Ampudia had summoned them to assert a common Catholicism, come across the river, cease “to defend a robbery and usurpation which, be assured, the civilized nations of Europe look upon with the utmost indignation,” and settle down on a generous land bounty. Some of them did so, and the St. Patrick Battalion of American deserters was eventually formed, fought splendidly throughout the war, and was decimated in the campaign for Mexico City — after which its survivors were executed in daily batches.… This earliest shooting of deserters as they swam the Rio Grande, an unwelcome reminder that war has ugly aspects, at once produced an agitation. As soon as word of it reached Washington, the National Intelligencer led the Whig press into a sustained howl about tyranny. In the House J. Q. Adams rose to resolve the court-martial of every officer or soldier who should order the killing of a soldier without trial and an inquiry into the reasons for desertion. He was voted down but thereafter there were deserters in every Whig speech on the conduct of the war, and Calm Observer wrote to all party papers that such brutality would make discipline impossible. But a struggling magazine which had been founded the previous September in the interest of sports got on a sound financial footing at last. The National Police Gazette began to publish lists of deserters from the army, and the War Department bought up big editions to distribute among the troops. Taylor sat in his field works writing prose. Ampudia’s patrols reconnoitered the camp and occasionally perpetrated an annoyance. Taylor badly needed the Texas Rangers, a mobile force formed for frontier service in the Texas War of Independence and celebrated ever since. It was not yet available to him, however, and he was content to send out a few scouts now and then. So Colonel Truman Cross, the assistant quartermaster general, did not return from one of his daily rides. He was still absent twelve days later, and Lieutenant Porter, who went looking for him with ten men, ran into some Mexican foragers and got killed.

Government is a contrivance of human wisdom to provide for human wants," wrote Edmund Burke in his Reflections on the Revolution in France. In the original and primary sense of lacks or needs, wants tend to structure our vision of government's responsibilities. The quest for security - whether economic, physical, psychological, or military - brings a sense of urgency to politics and is one of the enduring sources of passion in policy controversies. Need is probably the most fundamental political claim. Even toddlers know that need carries more weight than desire or deservingness. They learn early to counter a rejected request by pleading, "I need it." To claim need is to claim that one should be given the resources or help because they are essential. Of course, this raises the question "essential for what?" In conflicts over security, the central issues are what kind of security government should attempt to provide; what kinds of needs it should attempt to meet; and how the burdens of making security a collective responsibility should be distributed. Just as most people are all for equity and efficiency in the abstract, most people believe that society should help individuals and families when they are in dire need. But beneath this consensus is a turbulent and intense conflict over how to distinguish need from mere desire, and how to preserve a work - or - merit based system of economic distribution in the face of distribution according to need. Defining need for purposes of public programs become much an exercise like defining equity and efficiency. People try to portray their needs as being objective, and policymakers seek to portray their program criteria as objective, in order to put programs beyond political dispute. As with equity and efficiency, there are certain recurring strategies of argument that can be used to expand or contract a needs claim. In defense policy, relative need is far more important than absolute. Our sense of national security (and hence our need for weapons) depends entirely on comparison with the countries we perceive as enemies. And here Keynes is probably right: The need for weapons can only be satisfied by feeling superior to "them." Thus, it doesn't matter how many people our warheads can kill or how many cities they can destroy. What matters is what retaliatory capacity we have left after an attack by the other side, or whether our capacity to sustain an offense is greater than their capacity to destroy it. The paradox of nuclear weapons is that the more security we gain in terms of absolute capability (i.e., kill potential), the more insecure we make ourselves with respect to the consequences of nuclear explosions. We gain superiority only by producing weapons we ourselves are terrified to use.

In the contemporary world there are two classes of bad plans-the plans invented and put into practice by men who do not accept our ideal postulates, and the plans invented and put into practice by the men who accept them, but imagine that the ends proposed by the prophets can be achieved by wicked or unsuitable means. Hell is paved with good intentions, and it is probable that plans made by well-meaning people of the second class may have results no less disastrous than plans made by evil-intentioned people of the first class. Which only shows, yet once more, how right the Buddha was in classing unawareness and stupidity among the deadly sins. Let us consider a few examples of bad plans belonging to these two classes. In the first class we must place all Fascist and all specifically militaristic plans. Fascism, in the words of Mussolini, believes that "war alone brings up to its highest tension all human energy and puts the stamp of nobility upon the peoples who have the courage to meet it." Again, "a doctrine which is founded upon the harmful postulate of peace is hostile to Fascism." The Fascist, then, is one who believes that the bombardment of open towns with fire, poison and explosives (in other words, modern war) is intrinsically good. He is one who rejects the teaching of the prophets and believes that the best society is a national society living in a state of chronic hostility towards other national societies and preoccupied with ideas of rapine and slaughter. He is one who despises the non-attached individual and holds up for admiration the person who, in obedience to the boss who happens at the moment to have grabbed political power, systematically cultivates all the passions (pride, anger, envy, hatred) which the philosophers and the founders of religions have unanimously condemned as the most maleficent, the least worthy of human beings. All fascist planning has one ultimate aim: to make the national society more efficient as a war machine. Industry, commerce and finance are controlled for this purpose. The manufacture of substitutes is encouraged in order that the country may be self-sufficient in time of war. Tariffs and quotas are imposed, export bounties distributed, exchanges depreciated for the sake of gaining a momentary advantage or inflicting loss upon some rival. Foreign policy is conducted on avowedly Machiavellian principles; solemn engagements are entered into with the knowledge that they will be broken the moment it seems advantageous to do so; international law is invoked when it happens to be convenient, repudiated when it imposes the least restraint on the nation's imperialistic designs. Meanwhile the dictator's subjects are systematically educated to be good citizens of the Fascist state. Children are subjected to authoritarian discipline that they may grow up to be simultaneously obedient to superiors and brutal to those below them. On leaving the kindergarten, they begin that military training which culminates in the years of conscription and continues until the individual is too decrepit to be an efficient soldier. In school they are taught extravagant lies about the achievements of their ancestors, while the truth about other peoples is either distorted or completely suppressed. the press is controlled, so that adults may learn only what it suits the dictator that they should learn. Any one expressing un-orthodox opinions is ruthlessly persecuted. Elaborate systems of police espionage are organized to investigate the private life and opinions of even the humblest individual. Delation is encouraged, tale-telling rewarded. Terrorism is legalized. Justice is administered in secret; the procedure is unfair, the penalties barbarously cruel. Brutality and torture are regularly employed.

Details aside, the frequency-of-seeing experiment brings forward a beautiful idea: the probabilistic nature of our perceptions reflects the physics of random photon arrivals. An absolutely crucial point is that Hecht, Shlaer, and Pirenne chose stimulus conditions such that the five to seven photons needed for seeing were distributed across a broad area on the retina, an area that contains hundreds of photoreceptor cells. Thus, the probability of one receptor (rod) cell receiving more than one photon is very small. The experiments on human behavior therefore indicate that individual photoreceptor cells generate reliable responses to single photons. In fact, vision begins (as we discuss in more detail soon) with the absorption of light by the visual pigment rhodopsin, and so sensitivity to single photons means that each cell is capable of responding to a single molecular event. This is a wonderful example of using macroscopic experiments to draw conclusions about single cells and their microscopic mechanisms.

If someone who have read hundreds of books gives an average rating of below 3, they probably want to signal that they have a high standard, that only the best books they read will be honored with four or five stars. But it might as well indicate that they not only do not know how to find books in their own taste, but are actually drawn to reading books that are not really good according to them. If someone repeatedly read books they do not like are they masochists or do they really like reading books? If you randomly pick hundreds of books, you would give an average score of over 3 or higher. If publishers had done their work. Given a normal distribution of a score of 1 to 5 3 will be at the center of the bell curve. But maybe even higher since you would expect publishers to weed out books they would consider a 1 and publish books they consider a 3 or more. For example the drivers in a taxi service receive on average a score of 5. Drivers who have a score lower than 4.5 will be weeded out. So someone who spends hundreds of hours reading books but gives them an average score of below 3. Should statistically speaking be good at picking bad books. Or bad at picking good books or don't enjoy reading books. Than one might than wonder, if they don't enjoy reading books on average, than why are they reading?

the concept of median used in medical research does not characterize a probability distribution.

Die-Face Analysis In the 1930s, J. B. Rhine and his colleagues recognized and took into account the possibility that some dice studies may have been flawed because the probabilities of die faces are not equal. With some dice, it is slightly more likely that one will roll a 6 face than a 1 face because the die faces are marked by scooping out bits of material. The 6 face, for example, has six scoops removed from the surface of that side of the die, so it has slightly less mass than the other die faces. On any random toss, that tiny difference in mass will make the 6 slightly more likely to land face up, followed in decreasing probability by the 5, 4, 3, 2, and 1 faces. Thus, an experiment that relied exclusively upon the 6 face as the target may have been flawed because, unless there were also control tosses with no mental intention applied, we could not tell whether above-chance results were due to a mind-matter interaction or to the slightly higher probability of rolling a 6. To see whether this bias was present in these dice studies, we sifted out all reports for which the published data allowed us to calculate the effective hit rate separately for each of the six die faces used under experimental and control conditions. In fact, the suspected biases were found, as shown in figure 8.3. The hit rates for both experimental and control tosses tended to increase from die faces 1 to 6. However, most of the experimental hit rates were also larger than the corresponding control hit rates, suggested some thing interesting beyond the artifacts caused by die-face biases. For example, for die face 6 the experimental condition was significantly larger than the control with odds against chance of five thousand to one. Figure 8.3. Relationship between die face and hit rates for experimental and control conditions. The error bars are 65 percent confidence intervals. Because of the evidence that the die faces were slightly biased, we examined a subset of studies that controlled for these dice biases—studies using design protocols where die faces were equally distributed among the six targets. We referred to such studies as the “balanced-protocol subset.” Sixty-nine experiments met the balanced-protocol criteria. Our examination of those experiments resulted in three notable points: there was still highly significant evidence for mind-matter interaction, with odds against chance of greater than a trillion to one; the effects were constant across different measures of experimental quality; and the selective-reporting “file drawer” required a twenty-to-one ratio of unretrieved, nonsignificant studies for each observed study. Thus chance, quality, and selective reporting could not explain away the results. Dice Conclusions Our meta-analysis findings led us to conclude that a genuine mind-matter interaction did exist with experiments testing tossed dice. The effect had been successfully replicated in more than a hundred experiments by more than fifty investigators for more than a half-century.

Wal-Mart was too small and insignificant for any of the big boys to notice, and most of the promoters weren’t out in our area so we weren’t competitive. That helped me get access to a lot of information about how they were doing things. I probably visited more headquarters offices of more discounters than anybody else—ever. I would just show up and say, “Hi, I’m Sam Walton from Bentonville, Arkansas. We’ve got a few stores out there, and I’d like to visit with Mr. So-and-So”—whoever the head of the company was—“about his business.” And as often as not, they’d let me in, maybe out of curiosity, and I’d ask lots of questions about pricing and distribution, whatever. I learned a lot that way.

That’s the other, far more optimistic lesson of Price’s law and the Pareto distribution: those who start to have will probably get more.

Philosophically, I may view the world as deterministic, but in practice I have to accept that I am far from omniscient and even farther from omnipotent. Accepting that everything is effectively uncertain and that my thoughts, hopes, and actions can at best indirectly influence the world by influencing probability distributions: this has brought me a kind of peace through acceptance, and a greater mastery over the world around me. What can I do to control an outcome? That’s the wrong question. What can I do to influence the odds? Now that’s productive. That I can work with – in my life and in my job.

Here, Veblen’s iconoclasm showed its range, as he simultaneously exposed modern corporations as hives of swarming parasites, derided marginalism for disingenuously sanitizing these infested sites by rebranding nonproductivity as productivity, and attacked economists for failing to situate themselves historically. On Veblen’s account, the business enterprise was no more immune from historical change than any other economic institution. As the controlling force in modern civilization, the business enterprise too would necessarily undergo “natural decay” and prove “transitory.” Where history was heading next, however, Veblen felt he could not say, because no teleology was steering the evolutionary process as a whole, only (as he had said before) the “discretionary action of the human agents,” whose institutionally shaped choices were still unformed. Nevertheless, limiting himself to the “calculable future”—to what, in light of existing scientific knowledge, seemed probable in the near term—Veblen pointed to two contrasting possibilities, both beyond the ken of productivity theories. One alternative was militarization and war—barbarism redux. According to Veblen, the business enterprise, as its grows, spills over national boundaries and fosters the expansion of a world market in which “the business men of one nation are pitted against those of another and swing“the forces of the state, legislative, diplomatic, and military, against one another in the strategic game of pecuniary advantage.” As this game intensifies, competing nations rush (said Veblen presciently) to amass military hardware that can easily fall under the control of political leaders who embrace aggressive international policies and “warlike aims, achievements, [and] spectacles.” Unchecked, these developments could, he believed, demolish “those cultural features that distinguish modern times from what went before, including a decline of the business enterprise itself.” (In his later writings from the World War I period, Veblen returned to these issues.) The second future possibility was socialism, which interested Veblen (for the time being) not only as an institutional alternative to the business enterprise but also as a way of economic thinking that nullified the productivity theory of distribution. In cycling back to the phenomenon of socialism, which he had bracketed in The Theory of the Leisure Class, Veblen zeroed in on men and women who held industrial occupations, in which he observed a growing dissatisfaction with the bedrock institutions of the modern age. This discontent was socially concentrated, found not so much among laborers who were “mechanical auxiliaries”—manual extensions—“of the machine process“ but “among those industrial classes who are required to comprehend and guide the processes.” These classes consist of “the higher ranks of skilled mechanics and [of people] who stand in an engineering or supervisory ”“relation to the processes.” Carrying out these jobs, with their distinctive task requirements, inculcates “iconoclastic habits of thought,” which draw men and women into trade unions and, as a next step, “into something else, which may be called socialism, for want of a better term.” This phrasing was vague even for Veblen, but he felt hamstrung because “there was little agreement among socialists as to a programme for the future,” at least aside from provisions almost “entirely negative.

There are moments in an election battle, as in life, when all the possible pathways save one are suddenly closed; when what felt like a wide distribution of probable outcomes narrows to the inevitable.

Who’s distributing these anyway?” I inquire with a hint of suspicion. Kaye shrugs her shoulders nonchalantly. “I don’t know. There was a bunch of them in the lounge with a sign that said ‘take me’.” “So we’re eating cookies from an unknown source?” I tear off Santa’s head, narrowing my eyes at his jolly little smile. “How do we know these aren’t poisoned?” “This is college, Chris. They’re just cookies. Someone’s grandma probably sent them.” “Oh, so we’re eating someone’s stale re-gifted cookies then. These will be delicious,” I deadpan. “You’re so dramatic.

When we say that cage-free egg production costs only 10% to 20% more to produce at the level of retail (not farm) prices, we are assuming that the same distribution system is used for cage and cage-free eggs. When both cage-free and cage eggs are sold, it likely costs more to distribute cage-free eggs. The cage-free sector is small, prohibiting them from realizing the economies of scale enjoyed by the cage egg sector. Also, they are often different types of eggs. Studies have shown that about half of this 57% pre- mium charged for cage-free eggs is due to the fact that cage-free eggs tend to be brown eggs instead of white eggs. Consumers value brown eggs more, and stores have learned that when they bundle brown eggs with a cage-free production system they can charge particularly high prices. Moreover, cage-free eggs are often targeted to more affluent consumers and come in more elaborate packaging. In economics, this is referred to as price discrimination, and grocery stores probably charge a higher premium for cage-free eggs partly because they can.

By 1982, it had concluded that even the company’s earlier dire estimates were probably too low. That year, in a corporate document marked “not to be distributed externally” but given “wide circulation to Exxon management,” the company’s scientists concluded that heading off global warming would “require major reductions in fossil fuel combustion.” Otherwise, it concluded, “there are some potentially catastrophic events that must be considered.

Black swans are consequential events for which the underlying probability distribution is simply not known, or at least not known with any degree of certainty or reliability. In Taleb’s words, “Nothing in the past can convincingly point to [a black swan’s] possibility.”43

Perhaps the fundamental precept of probabilistic analysis is the exhortation to take a bird’s-eye, distributional view of the situation under analysis (e.g., a dice game, the traffic in Boulder, crimes in Pittsburgh, the situation with that troublesome knee) and to define a sample space of all the possible events and their logical, set membership interrelations. This step is exactly where rational analysis and judgments based on availability, similarity, and scenario construction diverge: When we judge intuitively, the mind is drawn to a limited, systematically skewed subset of the possible events. In the case of scenario construction, for example, we are often caught in our detailed scenario—focused on just one preposterously specific outcome path.

In 2018, Small Arms Survey reported that there are over one billion small arms distributed globally, of which 857 million (about 85 percent) are in civilian hands. The Small Arms Survey stated that U.S. civilians alone account for 393 million (about 46 percent) of the worldwide total of civilian held firearms." Guns are beautiful, but not often used in beautiful ways. I think our enlightened friends throughout the cosmos have very good reason not to pick our calls. If we had the capability, we would probably try to conquer them too.

We fundamentally changed the point of view of the business from customer-oriented to buyer-oriented. I put our buyers in charge of the company. From 1958 through 1976, we tried to carry what the customers asked for, given the limits of our small stores and other operational parameters. Each store manager had great latitude in what was carried and from what supplier it was ordered. There was very little central distribution except for Trader Joe’s labeled California wines or imports. Each store probably had access to ten thousand stock keeping units (SKUs), of which about three thousand were actually stocked in any given week. By the time I left in 1989, we were down to a band of 1,100 to 1,500 SKUs, all of which were delivered through a central distribution system. The managers no longer had any buying discretion and there were no “DSDs,” or direct store deliveries. And along the way not only did we drop a lot of products that our customers would have liked us to sell, even at not-outstanding prices, but we stopped cashing checks in excess of the amount of purchase, we stopped all full-case discounts, and we persistently shortened the hours. We violated every received-wisdom of retailing except one: we delivered great value, which is where most retailers fail.

If you were superneurotic about getting to the airport, you could use the same technique. Suppose you drove to the airport nine hundred times and estimate airport-travel volatility: the range of time it usually takes to get there is twenty to forty minutes. You’d also notice that a three-hour airport trip caused by a major traffic accident is less probable. It only happens 1–2 percent of the time. The traffic accident is called a “tail risk” because a three-hour trip is so unlikely it is in the tail of normal distribution.

We intuitively know that the heart is the center of love and empathy, and studies are showing this to be true. In fact, empathy manifests in the electromagnetic field (EMF), which is generated by the heart in amounts greater than anywhere else in the body. The heart’s EMF emits fifty thousand femtoteslas (a measure of EMF), in contrast to the ten generated by the brain.37 Other research shows that when separated from the magnetic field, the heart’s electrical field is sixty times greater in amplitude than the brain’s field.38 Through this field, a person’s nervous system tunes in to and responds to the magnetic fields produced by the hearts of other people.39 The heart’s field is therefore one of the means by which a practitioner affects patients. This effect leads to the question, What do you want to share? To generate positive outcomes for a patient, a practitioner must hold positive feelings in his or her own heart. Not only does good will profit the client, but it also benefits the practitioner as a person. A set of studies by researcher Dr. Rollin McCraty of the HeartMath Institute in California, and described in his e-book, The Energetic Heart, helps explain the importance of positive energy.40 For decades, scientists have known that information is encoded in the nervous system in the time intervals between activities or in the pattern of electrical activity. Recent studies also reveal that information is captured in hormone pulses. Moreover, there is a hormone pulse that coincides with heart rhythms, which means that information is also shared in the interbeat intervals of the pressure and electromagnetic waves produced by the heart. Negative emotions such as anger, frustration, or anxiety disturb the heart rhythm. Positive emotions such as appreciation, love, or compassion produce coherent or functional patterns. Feelings, distributed throughout the body, produce chemical changes within the entire system. Do you want to be a healthy person? Be sincerely positive as often as you can. You thus “increase the probability of maintaining coherence and reducing stress, even during challenging situations.”41 What you as a practitioner believe will be shared—everywhere and with everyone you meet.

Black swans are consequential events for which the underlying probability distribution is simply not known, or at least not known with any degree of certainty or reliability. In Taleb’s words, “Nothing in the past can convincingly point to [a black swan’s] possibility.

Since the 1970s, analyses of the public debt have suffered from the fact that economists have probably relied too much on so-called representative agent models, that is, models in which each agent is assumed to earn the same income and to be endowed with the same amount of wealth (and thus to own the same quantity of government bonds). Such a simplification of reality can be useful at times in order to isolate logical relations that are difficult to analyze in more complex models. Yet by totally avoiding the issue of inequality in the distribution of wealth and income, these models often lead to extreme and unrealistic conclusions and are therefore a source of confusion rather than clarity.

Harvard, and most other elite private schools, claim that their admissions are merit-based and need-blind, and that everyone who qualifies will receive enough financial aid to attend. This is bullshit, of course. If your parents went to Harvard (or another Ivy League university, such as Yale, Princeton, etc.) and have donated money, or if your father runs a huge global bank or is prime minister somewhere, your chances are surely somewhat improved. But forget about that—just look at the money and the students. In the 2011 academic year, Harvard’s administration proudly announced that slightly over 60 percent of its undergraduates received some level of financial aid and also stated that no student whose family earned less than $180,000 per year would be required to pay more than 10 percent of their total costs.17 Think about that for a minute. If you’re a Harvard student who receives no financial aid at all, you come from a family that makes much more than $180,000 per year. Let’s say the eligibility cutoff for receiving any financial aid at all is $300,000 (Harvard doesn’t reveal the number). This means that nearly 40 percent of Harvard undergraduates came from families whose income is at the very upper end of the American income distribution. This means that Harvard’s income distribution is probably even more skewed than America’s: in the nation as a whole, in 2010 the top 1 percent of families received about 20 percent of all annual income.

Actually, during this whole early period, Wal-Mart was too small and insignificant for any of the big boys to notice, and most of the promoters weren’t out in our area so we weren’t competitive. That helped me get access to a lot of information about how they were doing things. I probably visited more headquarters offices of more discounters than anybody else—ever. I would just show up and say, “Hi, I’m Sam Walton from Bentonville, Arkansas. We’ve got a few stores out there, and I’d like to visit with Mr. So-and-So”—whoever the head of the company was—“about his business.” And as often as not, they’d let me in, maybe out of curiosity, and I’d ask lots of questions about pricing and distribution, whatever. I learned a lot that way. KURT

Paul follows precisely the same strategy in dealing with the problem of eating food sacrificed to idols. Meat was a precious and rare commodity in an ancient city. Most people could not afford to buy it in the market. The main time they would eat meat would be at a sacrificial festival provided either by the city or more often by a wealthy individual who paid for the festival and its expenses out of his own pocket in return for the honor he and his family would then gain. The sacrifices would be made, some of the materials would be burned for the god, some would be given to the priests or other officials of the cult, and then the rest would be distributed to the people for their own feasting with their families and friends. But of course, any participation in these activities was precisely what Jews and early Christians considered idolatry. The poor Christians at Corinth would have had to attend a sacrificial setting in order to eat meat, and it would have been meat that had been sacrificed to a deity. The more “superstitious” Christians, no doubt, probably believed that the god, perhaps in the form of a “demon,” could have “possessed” the meat, and that by eating it, they could endanger themselves with demonic possession. They did believe, in at least some contexts and in some sense, that when they ate the “body and blood” of Christ in the Lord’s Supper, they were ingesting Christ himself. Why wouldn’t a similar process take place if they ate the sacrificial foods of Apollo or Aphrodite, two of the most important and powerful gods of Corinth? Even meat sold in a marketplace likely would have come from some kind of sacrificial practice. The officials or priests who were given portions of the sacrificed animal—often choice portions—had the liberty of making a bit of money by selling their portions to a butcher, who would then process the meat and resell it to people. In other words, unless one were rich enough to buy an animal and have it butchered and prepared, one could scarcely avoid eating meat that had been part of a sacrifice. The poor could hardly do so if they ate meat at all.

Indeed, in many agricultural regions — including northern China, southern India (as well as the Punjab), Mexico, the western United States, parts of the Middle East, and elsewhere — water may be much more of a constraint to future food production than land, crop yield potential, or most other factors. Developing and distributing technologies and practices that improve water management is critical to sustaining the food production capability we now have, much less increasing it for the future. Water-short Israel is a front-runner in making its agricultural economy more water-efficient. Its current agricultural output could probably not have been achieved without steady advances in water management — including highly efficient drip irrigation, automated systems that apply water only when crops need it, and the setting of water allocations based on predetermined optimum water applications for each crop. The nation’s success is notable: between 1951 and 1990, Israeli farmers reduced the amount of water applied to each hectare of cropland by 36 percent. This allowed the irrigated area to more than triple with only a doubling of irrigation water use.37 Whether

He had made a discovery of the first magnitude. It opened up an entirely new approach to physics, which led to statistical mechanics, to a proper understanding of thermodynamics and to the use of probability distributions in quantum mechanics. If he had done nothing else, this breakthrough would have been enough to put him among the world's great scientists.

Does the flat tax work?...The flat tax works in a country that is a former Communist state, with no investment capital, and low wage rates, which needs to build a capitalist economy from a base of approximately zero. The flat tax works if people are willing to pay a 20% sales tax on everything they buy to make up for lower revenue. The flat tax works if employers are willing to pay 34%, or more, in Social Security taxes for every employee they hire. The flat tax works in a country where almost everyone has the same amount of wealth so there's no need for the distributive effect of graduated rates. And if all these conditions are met, the flat-rate tax will probably work as long as the economy is on a path of steady growth.

They point out that we never know for sure which hypothesis is the true one, and so we shouldn’t just pick one hypothesis, like a value of 0.7 for the probability of heads; rather, we should compute the posterior probability of every possible hypothesis and entertain all of them when making predictions. The sum of the probabilities of all the hypotheses must be one, so if one becomes more likely, the others become less. For a Bayesian, in fact, there is no such thing as the truth; you have a prior distribution over hypotheses, after seeing the data it becomes the posterior distribution, as given by Bayes’ theorem, and that’s all.

In practice, quantum mechanics merely gives predictions with probabilities attached. This should be considered as a normal and quite acceptable feature of predictions made by science: different possible outcomes with different probabilities. In the world that is familiar to us, we always have such a situation when we make predictions. Thus the question remains: What is the reality described by quantum theories? I claim that we can attribute the fact that our predictions come with probability distributions to the fact that not all relevant data for the predictions are known to us, in particular important features of the initial state.

The field of the electron is real because it results from the laws of quantum mechanics and appropriate initial conditions. The laws determine the field's behavior-its propagation in space in particular. Just like the field of light, the field of an electron is nothing but that: a field. With each point in space, we associate a number that signifies it is a probability. The field equations tell us that their solution, the field from which we can calculate the probability distribution for finding the electron, is oscillatory. We know that there is no something that oscillates-it's just the field. The field of the electron is nothing but an excitation of empty space. The electron with its charge is just being thrown in-and it is ubiquitous.

The elementary particles are often dubbed the atoms of our day. That may or may not be correct. It might be an acceptable metaphor for a particle that is hidden in its probability distribution; it is less so for the distribution itself. We have no notion whether or not elementary particles such as electrons or quarks are ultimately divisible. We also don't know whether they have any internal structure or we can continue to deal with them as though their entire charge and mass were concentrated in one point. But the probability of finding particles can always be subdivided. Once we include the probability distributions discussed above, these atoms of modern times differ from those of the atomists in antiquity by an absence of sharply defined limits that separate things being from things not being, matter from empty space.

INTO AND OUT OF THE VACUUM To make real particles out of the virtual ones that are part of the vacuum fluctuations, the only thing needed is energy. But the energy inherent in the vacuum is inaccessible; it would have to be extracted from the vacuum, and that is impossible, because the vacuum is already the state of lowest energy. When an electron and a positron collide in the interaction region of the detector, the ensuing final-state volume is overall electrically neutral; in this sense, it is a vacuum. The uncertainty relation keeps us from knowing the precise locations of the particles along with their velocities; our probability of finding them is distributed through a certain spatial volume. If electrons and positrons were classical particles, they could obviously not annihilate each other; no provision at all is made in classical physics for processes of this kind. Quantum mechanics, however, permits us to look at them at though they were both a particle and a hole . When the particle drops into the hole- a process that is very likely under the circumstances-the sum of their motion energy and mass energy will be freed.

These are the four principal components of the SEU model: a cardinal utility function, an exhaustive set of alternative strategies, a probability distribution of scenarios for the future associated with each strategy, and a policy of maximizing expected utility.

On the one hand, there was the primeval institution of the sacrifice and the egalitarian distribution and communal consumption of its roast meat—a ritual expression of tribal solidarity before deity probably inherited from the most distant Indo-European past.9 This was the institution that governed the “long-term transactional order.” On the other, there were the conventions of reciprocal gift-exchange and of booty distribution. These were the rules that governed the “short-term transactional order,” concerned not with cosmic order and harmony between the classes but with the more mundane matter of ensuring that the everyday business of primitive society—drinking and hunting when at peace; rape and pillage when at war—did not dissolve into chaos.

Freed of the burden I had been carrying, I moved on, this time circling east. Under an overpass at Nogizaka, north of Roppongi-dori, I saw a half-dozen chinpira, gaudy in sleek racing leathers, squatting in a tight semicircle, their low-slung metal motorcycles parked on the footpath alongside them. Fragments of their conversation skipped off the concrete wall to my right, the words unintelligible but the notes tuned as tight as the tricked-out exhaust pipes of their machines. They were probably jacked on kakuseizai, the methamphetamine that has been the Japanese drug of choice since the government distributed it to soldiers and workers during World War II, and of which these chinpira were doubtless both purveyors and consumers. They were waiting for the drug-induced hum in their muscles and brains to hit the right pitch, for the hour to grow suitably late and the night more seductively dark, before emerging from their concrete lair and answering the neon call of Roppongi. I watched them take notice of me, a solitary figure approaching from the southern end of what was in effect a narrow tunnel. I considered crossing the street, but a metal divider made that maneuver unfeasible. I might simply have backed up and taken a different route. My failure to do so made it more difficult for me to deny that I was indeed heading toward the cemetery.

Whenever liquid water makes the transition to ice, energy is given off to the surroundings. In the process, the water itself assumes a state that is both more ordered and lower in energy. It is a general rule that any system that can give off heat and thereby assume a state of lower energy will do so. For the purpose of illustration, let's assume that the energy set free by the freezing of water is extremely high-so high that it surpasses the energy that is by virtue of Albert Einstein's E = mc^2 connected with the very existence of the water molecules. What would happen? In this fictitious case, it would pay energetically if water in the form of ice were spontaneously created from a space that beforehand contained no water at all. Thus there would be a certain probability for this to occur-never mind that anti-ice would have to be produced too. Let's imagine that it occurs: a crystal of ice is created spontaneously out of the void. Like every crystal, it would have some preferred direction in space and a certain location. Consequently, the perfect symmetry of space would be broken. These imagined circumstances do not exist in reality as far as ice is concerned, but they apply roughly for one of the most imaginative constructs of physics-the so-called Higgs field. This field appears spontaneously in a void as its walls are cooled down-starting from the absurdly high temperature of 10^15 degrees. The field will appear in an ordered state; for a poetic simile, think of ice flowers growing on a window. The energy needed for its existence is smaller than the energy liberated by its falling into that ordered pattern. This pattern is not to be understood in terms of spatial geometry; rather, it refers to the abstract space made up of the properties of elementary particles. In geometrical space, it is merely a field resembling a particularly simple distribution; to every point in space, we assign one and the same complex number. This implies that the Higgs field does not break geometrical symmetry-it breaks an abstract symmetry of elementary particles. In fact, it was introduced into modern theoretical physics by the Scottish physicist Peter Higgs for that very reason-to break an abstract symmetry that would not permit elementary particles to have masses.

Carol Bell, a British academician, has recently observed that “the strategic importance of tin in the LBA [Late Bronze Age] … was probably not far different from that of crude oil today.”3 At that time, tin was available in quantity only from specific mines in the Badakhshan region of Afghanistan and had to be brought overland all the way to sites in Mesopotamia (modern Iraq) and north Syria, from where it was distributed to points farther north, south, or west, including onward across the sea to the Aegean. Bell continues, “The availability of enough tin to produce … weapons grade bronze must have exercised the minds of the Great King in Hattusa and the Pharaoh in Thebes in the same way that supplying gasoline to the American SUV driver at reasonable cost preoccupies an American President today!

Education is probably the single greatest factor in determining economic success and subsequent freedom in our society.

There are C(n, k) ways to distribute a given event k-times in a string of n events. Hence, and now comes the grand moment, the probability that a certain event, occurring with the probability p, occurs k times within n trials is thus: P = C(n, k) · pk · (1-p)n-k And that! Ladies and gentleman, is the formula for the binomial distribution in all its glory. If

Miss Manners’ mother always told her to travel either first or third class, but never second, when crossing. (Not crossing class lines, silly; crossing the Atlantic Ocean, in the days when that was done properly, with bouillon at eleven on the promenade deck and tea at five in the salon.) In first class, in those days, you had luxury; in third class, you had fun. This is the proper distribution of the world’s blessings. In second class, you had neither. Naturally, then, someone invented the one-class ship, where the advantages of second class could be enjoyed by all, which is probably why we have those overanxious things called airplanes for crossings these days. You

By the Markovian and stationary properties of the CTMC, the probability that the CTMC leaves state i in the next t seconds is independent of how long the CTMC has already been in state i. That is, P{τi > t + s | τi > s} = P{τi > t} . Question: What does this say about τi? Answer: This says that τi is memoryless. But this means τi is Exponentially distributed!

A CTMC is a stochastic process with the property that every time it enters state i, the following hold: 1.   The amount of time the process spends in state i before making a transition is Exponentially distributed with some rate (call it νi). 2.   When the process leaves state i, it will next enter state j with some probability (call it pij) independent of the time spent at state i.

πj represents the limiting probability that the chain is in state j (independent of the starting state i). For an M-state DTMC, with states 0, 1, . . . , M – 1, represents the limiting distribution of being in each state.

we never have to actually determine whether our DTMC is positive recurrent. It suffices to simply check for irreducibility and aperiodicity and then solve the stationary equations. If these stationary equations yield a distribution, then that distribution is also the limiting probability distribution.

Hunter-gatherer mothers rely on one another to help watch children,16 and males share meat extensively not just with their families but also with other men. When a hunter kills something large, like a several-hundred-pound antelope, he distributes meat to everyone in camp. This sort of sharing isn’t just an effort to be nice and to avoid waste; it’s a vital strategy to reduce the risk of hunger, because the chances of a hunter killing a large animal on any given day are small. By sharing meat on the days he hunts successfully, a hunter increases his chances of getting meat from fellow hunters on the days he comes home empty-handed. Men also sometimes hunt in groups to increase their probability of hunting success and to help one another carry home the bounty. Not surprisingly, hunter-gatherers are highly egalitarian and they place great stock in reciprocity, helping assure everyone a more regular supply of resources. Today

STUDENT: Can we even define free will? SCOTT: Yeah, that's an excellent question. It's very hard to separate the question of whether free will exists from the question of what the definition of it is. What I was trying to do is, by saying what I think free will is not, give some idea of what the concept seems to refer to. It seems to me to refer to some transition in the state of the universe where there are several possible outcomes, and we can't even talk coherently about a probability distribution over them. STUDENT: Given the history? SCOTT: Given the history. STUDENT: Not to beat this to death, but couldn't you at least infer a probability distribution by running your simulation many times and seeing what your free will entity chooses each time? SCOTT: I guess where it becomes interesting is, what if (as in real life) we don't have the luxury of repeated trials?

What should we impose if we want to avoid Grandfather Paradoxes? Right: that the output distribution should be the same as the input one. We should impose the requirement that Deutsch calls causal consistency: the computation within the CTC must map the input probability distribution to itself. In deterministic physics, we know that this sort of consistency can't always be achieved – that's just another way of stating the Grandfather Paradox. But as soon as we go to probabilistic theories, well, it's a basic fact that every Markov chain has at least one stationary distribution. In this case of the Grandfather Paradox, the unique solution is that you're born with probability ½, and if you're born, you go back in time and kill your grandfather. Thus, the probability that you go back in time and kill your grandfather is ½, and hence you're born with probability ½. Everything is consistent; there's no paradox.

FROM JACKSON TO HILLARY The full story, however, is told in Steve Inskeep’s recent book Jacksonland, which I will rely on for my subsequent account. “Jackson managed national security affairs in a way that matched his interest in land development,” Inskeep notes. “He shaped his real estate investments to complement his official duties, and performed his official duties in a way that benefited his real estate interests.”16 As Inskeep shows, typically Jackson would set his eye on a large tract of Indian territory. Then, even before chasing the Indians off that territory, Jackson would send surveyors in to assess the land in terms of its real estate value. Jackson would then alert his cronies, and together they would make a bid to purchase that real estate. In this way Jackson became a Tennessee plantation magnate and one of the largest slave owners in his home state. Jackson was a ruthless con artist who became fabulously wealthy by trading on his political office. Sound familiar? His career illustrates the familiar Democratic story of leaders making sure that when there are spoils to be distributed, the lion’s share goes to them. Obviously not all Democrats use their political positions to get rich, but a number of them, from Jackson himself to Lyndon Johnson to Bill Clinton, certainly did. Jackson’s true modern counterpart—as you have probably figured out by now—is Hillary Clinton. Their stories are closely parallel. If Hillary started out “dead broke,” as she claims she did, after her husband’s presidency, so did Jackson begin with nothing as an orphan. Neither of them became successful through starting and running a successful business. Rather, they cashed in on their political influence. Just as Jackson made money on land deals stemming from his success as a general, Hillary too figured out ways to enrich herself through her government positions, becoming fabulously wealthy in just a few years.

Climate change is a global problem with grave implications: environmental, social, economic, political and for the distribution of goods. It represents one of the principal challenges facing humanity in our day. Its worst impact will probably be felt by developing countries in coming decades. Many of the poor live in areas particularly affected by phenomena related to warming, and their means of subsistence are largely dependent on natural reserves and ecosystemic services such as agriculture, fishing and forestry. They have no other financial activities or resources which can enable them to adapt to climate change or to face natural disasters, and their access to social services and protection is very limited. For example, changes in climate, to which animals and plants cannot adapt, lead them to migrate; this in turn affects the livelihood of the poor, who are then forced to leave their homes, with great uncertainty for their future and that of their children. There has been a tragic rise in the number of migrants seeking to flee from the growing poverty caused by environmental degradation. They are not recognized by international conventions as refugees; they bear the loss of the lives they have left behind, without enjoying any legal protection whatsoever. Sadly, there is widespread indifference to such suffering, which is even now taking place throughout our world. Our lack of response to these tragedies involving our brothers and sisters points to the loss of that sense of responsibility for our fellow men and women upon which all civil society is founded.

The entrepreneurs who stuck with Silicon Valley learned four big lessons from the dot-com crash that still guide business thinking today: 1. Make incremental advances Grand visions inflated the bubble, so they should not be indulged. Anyone who claims to be able to do something great is suspect, and anyone who wants to change the world should be more humble. Small, incremental steps are the only safe path forward. 2. Stay lean and flexible All companies must be “lean,” which is code for “unplanned.” You should not know what your business will do; planning is arrogant and inflexible. Instead you should try things out, “iterate,” and treat entrepreneurship as agnostic experimentation. 3. Improve on the competition Don’t try to create a new market prematurely. The only way to know you have a real business is to start with an already existing customer, so you should build your company by improving on recognizable products already offered by successful competitors. 4. Focus on product, not sales If your product requires advertising or salespeople to sell it, it’s not good enough: technology is primarily about product development, not distribution. Bubble-era advertising was obviously wasteful, so the only sustainable growth is viral growth. These lessons have become dogma in the startup world; those who would ignore them are presumed to invite the justified doom visited upon technology in the great crash of 2000. And yet the opposite principles are probably more correct: 1. It is better to risk boldness than triviality. 2. A bad plan is better than no plan. 3. Competitive markets destroy profits. 4. Sales matters just as much as product.

day, the trigger was an older woman with deep wrinkles. To this day, I cannot be certain about what caused her to react so strongly. Perhaps she had used up her patience simmering in the sun for hours at the back of the line. Perhaps she had some desperately hungry grandchildren who she needed to get back to. It is impossible to know exactly what happened. But after she received her allocation of wheat, she broke the established rules of the feeding site and moved toward Bubba. She looked up at him and unleashed a verbal attack. Bubba, as gentle as ever, simply smiled at her. The more he smiled, the angrier she got. I noticed the commotion when our Somali guards suddenly tensed and turned toward the disturbance. All I could see was Bubba, head and shoulders above a gathering crowd, seemingly unperturbed, and smiling down at someone. His patient response only fueled the woman’s rage. I heard her sound of fury long before I spotted the source when she launched a long stream of vile curses at Bubba. Thankfully, he didn’t understand a word that she was saying. It was now possible to understand her complaint. She was upset about the quality of the “animal feed” that was being distributed for human consumption. She was probably right in her assessment of the food. These were surplus agricultural products that United Nations contributing members didn’t want, couldn’t sell, and had no other use for. As this hulking American continued to smile, the woman realized that she was not communicating. Now, furious and frustrated, she bent down, set her plastic bag on the ground, grabbed two fistfuls of dirty, broken wheat, grain dust, dirt and chaff. She straightened to her full height and flung the filthy mixture as hard as she could into Bubba’s face. The crowd was deathly silent as I heard a series of loud metallic clicks that indicated that an entire squad of American soldiers had instinctively locked and loaded all weapons in readiness for whatever might happen next. Everything felt frozen in time as everyone waited and watched for Bubba’s reaction. A Somali man might have beaten the woman for such a public insult—and he would have considered his action and his anger entirely justified. I knew that Bubba had traveled half-way around the world at his own expense to spend three months of personal vacation time to help hurting people. And this was the thanks that he received? He was hot, sweaty, and drained beyond exhaustion—and he had just been publicly embarrassed. He had every reason to be absolutely livid. Instead, he raised one hand to rub the grit out of his eyes, and then he gave the woman one more big smile. At that point, he began to sing. And what he sang wasn’t just any song. She didn’t understand the words, of course. But she, and the entire crowd, stood in silent amazement as Bubba belted out the words to the 1950’s Elvis Presley rock-n-roll classic: You ain’t nothin’ but a hound dog Cryin’ all the time You ain’t nothin’ but a hound dog Cryin’ all the time Well, you ain’t never caught a rabbit And you ain’t no friend of mine. By the time he started singing the next verse, the old woman had turned and stomped off in frustration, angrily plowing a path through the now-smiling crowd of Somalis to make her escape. Watching her go, Bubba raised his voice to send her off with rousing rendition of the final verse: Well they said you was high-classed Well, that was just a lie Ya know they said you was high-classed Well, that was just a lie Well, you ain’t never caught a rabbit And you ain’t no friend of mine.

Why exactly has social mobility declined in the United States in the past thirty years, so that the probability has more than halved that a man born into the bottom 25 per cent of the income distribution will end his life in the top quartile?13 Once the United States was famed as a land of opportunity, where a family could leap from ‘rags to riches’ in a generation. But today, if you are born to parents in the bottom income quintile, you have just a 5 per cent chance of getting into the top quintile without a college degree.

marginal likelihood (i.e., the probability of the observed data) does not involve the parameter , and is given by a single number that ensures that the area under the posterior distribution equals 1.

A key point in my work: Randomness has more than one "state," or form, and each, if allowed to play out on a financial market, would have a radically different effect on the way prices behave. One is the most familiar and manageable form of chance, which I call "mild." It is the randomness of a coin toss, the static of a badly tuned radio. Its classic mathematical expression is the bell curve, or "normal" probability distribution-so-called because it was long viewed as the norm in nature. Temperature, pressure, or other features of nature under study are assumed to vary only so much, and not an iota more, from the average value. At the opposite extreme is what I call "wild" randomness. This is far more irregular, more unpredictable. It is the variation of the Cornish coastline-savage promontories, craggy rocks, and unexpectedly calm bays. The fluctuation from one value to the next is limitless and frightening. In between the two extremes is a third state, which I call "slow" randomness.

So why didn't ABCP investors -- at least the large institutional investors -- have a better grasp of the uncertain nature of market disruption triggers as defined under Canadian-style liquidity? Probably because the contracts were not available for review to investors wishing to purchase ABCP -- yet another example of the lack of transparency surrounding the distribution and sale of this product.

They have just concluded their business in the latest town, where Itempas nearly drowned trying to help a fishing boat haul in its catch with old fraying nets and a captain who did not heed the dire weather reports. Because other mortals’ lives were at stake, Itempas could use magic to save them, translocating everyone from the boat to the shore just as the mast sank beneath the waves. As a crowd gathers ’round to exclaim over the miracle of survivors, and to shout at the captain who sits ashamed nearby, Glee goes to her father, who stands watching all of this with a sterner-than-usual set to his face. There is more to it than the captain’s negligence, Glee understands. The boat’s nets were frayed because the captain could barely afford to keep his business afloat. His business was in danger because the price of fish is being artificially controlled by the Nobles’ Consortium in order to please several of the wealthier islander merchants, who run large fish distribution enterprises. The same people who curse the captain now have happily bought the cheap fish that made him so desperate for just one more catch. Now the man has lost his livelihood altogether, as have his crew members—but the price of fish will stay low, driving other captains into other storms and causing other wrecks from which there will be no magical rescue. It is painfully clear even to Glee, who has less of a jaded eye toward human foibles, that these people will never believe themselves complicit in the lives lost. They accept that this is the way the world works, in part because it is all they know and in part because it is all they wish to know. They are Itempans, probably, all of them. Comfortable with the status quo.

In some ways, the VaR debacle is the opposite of the Schlitz example in Chapter 5. Schlitz was operating with a known probability distribution

The t-distribution is actually a series, or “family,” of probability density functions that vary according to the size of our sample.

If I received a nickel for every time someone asked me, “How is LinkedIn going to make money?” during those days I probably wouldn’t have needed another revenue model! But I knew that we should ignore that fire, because (1) the lack of revenue wasn’t going to be the proximate cause of death unless it prevented us from raising money and (2) the product fire was far more urgent and required our focused attention. If we couldn’t find the distribution to acquire a critical mass of at least a million users, and build a product they found compelling enough to become regular users of the service (or at least respond to LinkedIn requests), the revenue model would be irrelevant.

The key is to combine new technologies with effective distribution to potential customers, a scalable and high-margin revenue model, and an approach that allows you to serve those customers given your probable resource constraints.

Mark Allin and Richard Burton started Capstone, their book-publishing venture, with high hopes. False modesty aside, they knew they were excellent editors, with a great track record at two publishing giants. I could vouch for Mark Allin’s profit-making abilities, since he gave me the idea for writing The 80/20 Principle, my bestselling book. Richard and Mark envisaged Capstone as a star venture, the leader in a new category of ‘funky business books’. They convinced me that this idea was plausible and I became their financial backer. I reckoned that I had an ‘each-way bet’ - either their star business would materialise, or, at worst, they would pick a few great winners, making Capstone highly profitable. The business appeared to start well. They commissioned a stream of trendy books from interesting authors. The product looked great, with distinctive trendy designs. Mark and Richard were full of ideas and enthusiasm, confidently projecting sales that would give us good profits. The only thing was, the forecasts never materialised. Whenever we looked at the numbers we were constantly disappointed. I kept injecting cash, and it kept vanishing. To this day I don’t know why their books didn’t sell in quantities we could reasonably expect.The favoured explanation was the weakness of the sales force - inevitably, it was difficult to acquire distribution muscle from scratch. Maybe they just had bad luck in not commissioning any smash hits. Whatever the reason, Capstone was a financial black hole. I remember a rather difficult meeting at my home in Richmond some three years after the start. Richard and Mark asked for a further loan to commission new books. I had to say no. We had to face facts. Capstone was not a star; the category of ‘funky business books’ had not established itself. Capstone was a rather weak follower in the business-books arena. Capstone had none of the financial attributes of a star. If it looked like a dog, behaved like a dog and barked like a dog, it probably was a dog.