Numerical Analysis Quotes

In essence, the algebra mindset transformed broken situations into dynamic opportunities for lasting impact. And it did so with elegant equations, precise numerals, and dynamic efficiency. The world would never be the same.

Well, the Taco Bell burrito scale of immense magnitude returned an 'r' factor of point eight six. Then when I applied the nose-picking coefficient, I discovered a multivariate numeration of nine dot oh sixteen on the Richter scale.

Sales is a constant state of information gathering and analysis. There are numerous factors that will affect your sale – from market position, to manufacturing capacity, to a seemingly harmless tidbit of information received over lunch. The more quality information you have, the better your analysis, and the better your sales results will be.

Don't worry, boss,” HARV said. “I get the feeling that this is only the tip of the iceberg of complications.” “HARV, you’re a machine. You don’t get feelings.” “Would it make you feel better if I said I've done a numerical analysis on the probabilities and the results are skewed toward you having more problems with this case?

The problem with this abbreviated analysis is that violent crime is not responsible for mass incarceration. As numerous researchers have shown, violent crime rates have fluctuated over the years and bear little relationship to incarceration rates—which have soared during the past three decades regardless of whether violent crime was going up or down.23 Today violent crime rates are at historically low levels, yet incarceration rates continue to climb.

Darwin himself said as much: 'If it could be demonstrated that any complex organ existed which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down. But I can find no such case.' Darwin could find no such case, and nor has anybody since Darwin's time, despite strenuous, indeed desperate, efforts. Many candidates for this holy grail of creationism have been proposed. None has stood up to analysis.

If we want to solve problems effectively...we must keep in mind not only many features but also the influences among them. Complexity is the label we will give to the existence of many interdependent variables in a given system. The more variables and the greater their interdependence, the greater the system's complexity. Great complexity places high demands on a planner's capacity to gather information, integrate findings, and design effective actions. The links between the variables oblige us to attend to a great many features simultaneously, and that, concomitantly, makes it impossible for us to undertake only one action in a complex system. A system of variables is "interrelated" if an action that affects or meant to affect one part of the system will also affect other parts of it. Interrelatedness guarantees that an action aimed at one variable will have side effects and long-term repercussions. A large number of variables will make it easy to overlook them. We might think of complexity could be regarded as an objective attribute of systems. We might even think we could assign a numerical value to it, making it, for instance, the product of the number of features times the number of interrelationships. If a system had ten variables and five links between them, then its "complexity quotient", measured in this way would be fifty. If there are no links, its complexity quotient would be zero. Such attempts to measure the complexity of a system have in fact been made. Complexity is not an objective factor but a subjective one. Supersignals reduce complexity, collapsing a number of features into one. Consequently, complexity must be understood in terms of a specific individual and his or her supply of supersignals. We learn supersignals from experience, and our supply can differ greatly from another individual's. Therefore there can be no objective measure of complexity.

Considered from this point of view, the fact that some of the theories which we know to be false give such amazingly accurate results is an adverse factor. Had we somewhat less knowledge, the group of phenomena which these "false" theories explain would appear to us to be large enough to "prove" these theories. However, these theories are considered to be "false" by us just for the reason that they are, in ultimate analysis, incompatible with more encompassing pictures and, if sufficiently many such false theories are discovered, they are bound to prove also to be in conflict with each other. Similarly, it is possible that the theories, which we consider to be "proved" by a number of numerical agreements which appears to be large enough for us, are false because they are in conflict with a possible more encompassing theory which is beyond our means of discovery. If this were true, we would have to expect conflicts between our theories as soon as their number grows beyond a certain point and as soon as they cover a sufficiently large number of groups of phenomena. In contrast to the article of faith of the theoretical physicist mentioned before, this is the nightmare of the theorist.

The brain is a machine, and the mind is a ghost within it. The origins of self-awareness and how the mind is able to perceive, analyze, and imagine are supposedly explained by numerous schools of psychology, although in fact they study only behavior through the gathering and the analysis of statistics. The why of the mind’s existence and the how of its profound capacity to reason—especially its penchant for moral reasoning—will by their very nature remain as mysterious as whatever lies outside of time.

The history of pi is only a small part of the history of mathematics, which itself is but a mirror of the history of man. That history is full of patterns and tendencies whose frequency and similarity is too striking to be dismissed as accidental. Like the laws of quantum mechanics, and in the final analysis, of all nature, the laws of history are evidently statistical in character. But what those laws are, nobody knows. Only a few scraps are evident. And of these is that the Heisels of Cleveland are more numerous than the Archimedes of Syracuse.

Almost nothing can be gained from pinball. The only payoff is a numerical substitution for pride. The loses, however, are considerable. You could probably erect bronze statues of every American president (assuming you are willing to include Richard Nixon) with the coins you will lose, while your lost time is irreplaceable. When you are standing before the machine engaged in your solitary act of consumption, another guy is plowing through Proust, while still another guy is doing some heavy petting with his girlfriend while watching "True Grit" at the local drive-in. They're the ones who may wind up becoming groundbreaking novelists or happily married men. No, pinball leads nowhere. The only result is a glowing replay light. Replay, replay, replay — it makes you think the whole aim of the game is to achieve a form of eternity. We know very little of eternity, although we can infer its existence. The goal of pinball is self-transformation, not self-expression. It involves not the expansion of the ego but its diminution. Not analysis but all-embracing acceptance. If it's self-expression, ego expansion or analysis you're after, the tilt light will exact its unsparing revenge. Have a nice game!

The human brain is by far the most complex object known to exist in the entire universe, containing more neurons than there are billions of stars in the Milky Way. The brain and the mind are very different things, and the latter is as mysterious as the former is complex. The brain is a machine, and the mind is a ghost within it. The origins of self-awareness and how the mind is able to perceive, analyze, and imagine are supposedly explained by numerous schools of psychology, although in fact they study only behavior through the gathering and the analysis of statistics. The why of the mind’s existence and the how of its profound capacity to reason—especially its penchant for moral reasoning—will by their very nature remain as mysterious as whatever lies outside of time.

In their book Warrior Lovers, an analysis of erotic fiction by women, the psychologist Catherine Salmon and the anthropologist Donald Symons wrote, "To encounter erotica designed to appeal to the other sex is to gaze into the psychological abyss that separates the sexes.... The contrasts between romance novels and porn videos are so numerous and profound that they can make one marvel that men and women ever get together at all, much less stay together and successfully rear children." Since the point of erotica is to offer the consumer sexual experiences without having to compromise with the demands of the other sex, it is a window into each sex's unalloyed desires. ... Men fantasize about copulating with bodies; women fantasize about making love to people. Rape is not exactly a normal part of male sexuality, but it is made possible by the fact that male desire can be indiscriminate in its choice of a sexual partner and indifferent to the partner's inner life--indeed, "object" can be a more fitting term than "partner." The difference in the sexes' conception of sex translates into a difference in how they perceive the harm of sexual aggression. ... The sexual abyss offers a complementary explanation of the callous treatment of rape victims in traditional legal and moral codes. It may come from more than the ruthless exercise of power by males over females; it may also come from a parochial inability of men to conceive of a mind unlike theirs, a mind that finds the prospect of abrupt, unsolicited sex with a stranger to be repugnant rather than appealing. A society in which men work side by side with women, and are forced to take their interests into account while justifying their own, is a society in which this thick-headed incuriosity is less likely to remain intact. The sexual abyss also helps to explain the politically correct ideology of rape. ... In the case of rape, the correct belief is that rape has nothing to do with sex and only to do with power. As (Susan) Brownmiller put it, "From prehistoric times to the present, I believe, rape has played a critical function. It is nothing more or less than a conscious process of intimidation by which all men keep all women in a state of fear." ... Brownmiller wrote that she adapted the theory from the ideas of an old communist professor of hers, and it does fit the Marxist conception that all human behavior is to be explained as a struggle for power between groups. But if I may be permitted an ad feminam suggestion, the theory that rape has nothing to do with sex may be more plausible to a gender to whom a desire for impersonal sex with an unwilling stranger is too bizarre to contemplate. Common sense never gets in the way of a sacred custom that has accompanied a decline of violence, and today rape centers unanimously insist that "rape or sexual assault is not an act of sex or lust--it's about aggression, power, and humiliation, using sex as the weapon. The rapist's goal is domination." (To which the journalist Heather MacDonald replies: "The guys who push themselves on women at keggers are after one thing only, and it's not reinstatement of the patriarchy.")

The bravest mob of independent fighters has little chance against a handful of disciplined soldiers, and the Church is perfectly logical in seeing her chief danger in the Encyclopaedia's systematised marshalling of scattered truths. As long as the attacks on her authority were isolated, and as it were sporadic, she had little to fear even from the assaults of genius; but the most ordinary intellect may find a use and become a power in the ranks of an organised opposition. Seneca tells us the slaves in ancient Rome were at one time so numerous that the government prohibited their wearing a distinctive dress lest they should learn their strength and discover that the city was in their power; and the Church knows that when the countless spirits she has enslaved without subduing have once learned their number and efficiency they will hold her doctrines at their mercy. —

My own odyssey of therapy, over my forty-five-year career, is as follows: a 750-hour, five-time-a-week orthodox Freudian psychoanalysis in my psychiatric residency (with a training analyst in the conservative Baltimore Washington School), a year’s analysis with Charles Rycroft (an analyst in the “middle school” of the British Psychoanalytic Institute), two years with Pat Baumgartner (a gestalt therapist), three years of psychotherapy with Rollo May (an interpersonally and existentially oriented analyst of the William Alanson White Institute), and numerous briefer stints with therapists from a variety of disciplines, including behavioral therapy, bioenergetics, Rolfing, marital-couples work, an ongoing ten-year (at this writing) leaderless support group of male therapists, and, in the 1960s, encounter groups of a whole rainbow of flavors, including a nude marathon group.

I am perpetually—sometimes darkly—amused by the workings of my mind, which can often seem less rational than I would like to believe they are. The human brain is by far the most complex object known to exist in the entire universe, containing more neurons than there are billions of stars in the Milky Way. The brain and the mind are very different things, and the latter is as mysterious as the former is complex. The brain is a machine, and the mind is a ghost within it. The origins of self-awareness and how the mind is able to perceive, analyze, and imagine are supposedly explained by numerous schools of psychology, although in fact they study only behavior through the gathering and the analysis of statistics. The why of the mind’s existence and the how of its profound capacity to reason—especially its penchant for moral reasoning—will by their very nature remain as mysterious as whatever lies outside of time.

The bravest mob of independent fighters has little chance against a handful of disciplined soldiers, and the Church is perfectly logical in seeing her chief danger in the Encyclopaedia's systematised marshalling of scattered truths. As long as the attacks on her authority were isolated, and as it were sporadic, she had little to fear even from the assaults of genius; but the most ordinary intellect may find a use and become a power in the ranks of an organised opposition. Seneca tells us the slaves in ancient Rome were at one time so numerous that the government prohibited their wearing a distinctive dress lest they should learn their strength and discover that the city was in their power; and the Church knows that when the countless spirits she has enslaved without subduing have once learned their number and efficiency they will hold her doctrines at their mercy. — The Church again," he continued, "has proved her astuteness in making faith the gift of grace and not the result of reason. By

Despite the popularity of this view, the DeValoises felt it was only a partial truth. To test their assumption they used Fourier's equations to convert plaid and checkerboard patterns into simple wave forms. Then they tested to see how the brain cells in the visual cortex responded to these new wave-form images. What they found was that the brain cells responded not to the original patterns, but to the Fourier translations of the patterns. Only one conclusion could be drawn. The brain was using Fourier mathematics—the same mathematics holography employed—to convert visual images into the Fourier language of wave forms. 12 The DeValoises' discovery was subsequently confirmed by numerous other laboratories around the world, and although it did not provide absolute proof the brain was a hologram, it supplied enough evidence to convince Pribram his theory was correct. Spurred on by the idea that the visual cortex was responding not to patterns but to the frequencies of various wave forms, he began to reassess the role frequency played in the other senses. It didn't take long for him to realize that the importance of this role had perhaps been overlooked by twentieth-century scientists. Over a century before the DeValoises' discovery, the German physiologist and physicist Hermann von Helmholtz had shown that the ear was a frequency analyzer. More recent research revealed that our sense of smell seems to be based on what are called osmic frequencies. Bekesy's work had clearly demonstrated that our skin is sensitive to frequencies of vibration, and he even produced some evidence that taste may involve frequency analysis. Interestingly, Bekesy also discovered that the mathematical equations that enabled him to predict how his subjects would respond to various frequencies of vibration were also of the Fourier genre.

Two observations take us across the finish line. The Second Law ensures that entropy increases throughout the entire process, and so the information hidden within the hard drives, Kindles, old-fashioned paper books, and everything else you packed into the region is less than that hidden in the black hole. From the results of Bekenstein and Hawking, we know that the black hole's hidden information content is given by the area of its event horizon. Moreover, because you were careful not to overspill the original region of space, the black hole's event horizon coincides with the region's boundary, so the black hole's entropy equals the area of this surrounding surface. We thus learn an important lesson. The amount of information contained within a region of space, stored in any objects of any design, is always less than the area of the surface that surrounds the region (measured in square Planck units). This is the conclusion we've been chasing. Notice that although black holes are central to the reasoning, the analysis applies to any region of space, whether or not a black hole is actually present. If you max out a region's storage capacity, you'll create a black hole, but as long as you stay under the limit, no black hole will form. I hasten to add that in any practical sense, the information storage limit is of no concern. Compared with today's rudimentary storage devices, the potential storage capacity on the surface of a spatial region is humongous. A stack of five off-the-shelf terabyte hard drives fits comfortable within a sphere of radius 50 centimeters, whose surface is covered by about 10^70 Planck cells. The surface's storage capacity is thus about 10^70 bits, which is about a billion, trillion, trillion, trillion, trillion terabytes, and so enormously exceeds anything you can buy. No one in Silicon Valley cares much about these theoretical constraints. Yet as a guide to how the universe works, the storage limitations are telling. Think of any region of space, such as the room in which I'm writing or the one in which you're reading. Take a Wheelerian perspective and imagine that whatever happens in the region amounts to information processing-information regarding how things are right now is transformed by the laws of physics into information regarding how they will be in a second or a minute or an hour. Since the physical processes we witness, as well as those by which we're governed, seemingly take place within the region, it's natural to expect that the information those processes carry is also found within the region. But the results just derived suggest an alternative view. For black holes, we found that the link between information and surface area goes beyond mere numerical accounting; there's a concrete sense in which information is stored on their surfaces. Susskind and 'tHooft stressed that the lesson should be general: since the information required to describe physical phenomena within any given region of space can be fully encoded by data on a surface that surrounds the region, then there's reason to think that the surface is where the fundamental physical processes actually happen. Our familiar three-dimensional reality, these bold thinkers suggested, would then be likened to a holographic projection of those distant two-dimensional physical processes. If this line of reasoning is correct, then there are physical processes taking place on some distant surface that, much like a puppeteer pulls strings, are fully linked to the processes taking place in my fingers, arms, and brain as I type these words at my desk. Our experiences here, and that distant reality there, would form the most interlocked of parallel worlds. Phenomena in the two-I'll call them Holographic Parallel Universes-would be so fully joined that their respective evolutions would be as connected as me and my shadow.

In 1941, Dorothy L. Sayers provided a detailed analysis of that creative process in The Mind of the Maker. She developed the relevance of the imago Dei for understanding artistic creation in explicitly trinitarian terms. In every act of creation there is a controlling idea (the Father), the energy which incarnates that idea through craftsmanship in some medium (the Son), and the power to create a response in the reader (the Spirit). These three, while separate in identity, are yet one act of creation. So the ancient credal statements about the Trinity are factual claims about the mind of the maker created in his image. Sayers delves into the numerous literary examples, in what is one of the most fascinating accounts ever written both of the nature of literature and of the imago Dei. While some readers may feel she has a tendency to take a good idea too far, The Mind of the Maker remains an indispensable classic of Christian poetics.

I see the world as a multi-layered, encrypted message—encrypted for countless reasons, by numerous sources. I believe our job as actively-engaged humans is to decode these messages for our own use and to document them for the greater body of human literature at the means each individual has at hand. As an artist—specifically, a cartoonist—that is the means/medium I use for my own decoding duties. Through my research, I use logic, reason and intellect to intuitively follow the knowledge thread that intrigues me, connecting the dots from pattern recognition, and producing the cartoons that form my socio-political analysis.

However, without its essential attributes the concept of ‘God’ is empty on its own. Like any other concept, it contains some essential features for your mind — at least God is either merely the Creator, or also Regulator of everything in the Universe, including your brain, mind and behavior. On the surface, maybe there is no serious distinction between them, since the majority looks at the surface only, the interchange of their meanings causes little or no discomfort for the intellect. But at the bottom there is clear-cut distinction between them. God as only the creator is the first cause of the Universe, which in turn also affects your brain and mind states through deterministic relationships between everything, visible or invisible for you, in the Universe. But even God itself cannot break that determinism and regulatory. In that context God is passive rather than active super power, he is not omnipotent, he can neither damn nor forgive you. Therefore, there is no need to worship, to perform numerous rituals, sacrifice, struggle for God against God’s enemies and so on and so forth. There is no appearance of any phenomenon, only the deep content related to ’emotional-motivational’ sub-system of mind such as the ultimate purpose of life and after death. The concept of ‘God’ with the meaning of just creator is more philosophical, and in some context more ‘scientific’, than the concept of 'God' with also the meaning of the regulator. In the former meaning you can substitute the concept of ‘energy’, ‘information’, ‘hard determinism’ and so on, in their broader sense, for the concept of ‘God’. But you cannot do it related to the latter meaning, because unlike the former, it is ideological rather than philosophical and ‘scientific’. There is no free thought there, there is no free conceptual analysis there, your contemplation cannot circulate in any direction only on the base of the logical investigation and logical argumentation. it is going to be confined at some point after which would come all-powerful God’s will, expressed in the holy scriptures, and ideological interpretation of that will according to various political-economic interests. (The Denotation and Connotation of the concept of God, Part 3)

To demand or preach mechanical precision, even in principle, in a field incapable of it, is to be blind and to mislead others," as the British liberal philosopher Isaiah Berlin noted in an essay on political judgement. Indeed what Berlin says of political judgement applies more broadly: judgement is a sort of skill at grasping the unique particularities of a situation, and it entails a talent for synthesis rather than analysis, "a capacity for taking in the total pattern of a human situation, of the way in which things hang together." A feel for the whole and a sense for the unique are precisely what numerical metrics cannot supply.

strictly stores data in several different data types, called ‘classes’: Numeric – e.g.

Zimbardo could not see the brutality himself because he was already too deep into his chosen role of Warden and lost his exterior view of his sociological “experiment”. He could not see clearly what was happening. More recently, Zimbardo has acted as a consultant to one of the arrested soldiers in the recent Abu Ghraib prison torture. He never denied the culpability of the individuals involved but was certain to bring up the lack of oversight and structure. In his recent book he states “Aberrant, illegal or immoral behavior by individuals in service professions, such as policemen, corrections officers, and soldiers, are typically labeled the misdeeds of “a few bad apples”. The implication is that they are a rare exception and must be set on one side of the impermeable line between evil and good, with the majority of good apples set on the other side. But who is making the distinction? Usually it is the guardians of the system, who want to isolate the problem in order to deflect attention and blame away from those at the top who may be responsible for creating untenable working conditions or for a lack of oversight or supervision. Again the bad-apple dispositional view ignores the apple barrel and its potentially corrupting situational impact on those within it. “A systems analysis focuses on the barrel makers, on those with the power to design the barrel.” Zimbardo isolated 7 social processes that grease the slippery slope of evil. I found myself in all of these seven steps, to a greater or lesser degree. They are: 1) Mindlessly taking the first step. 2) Dehumanization of others. 3) De-individualization of self (anonymity). 4) Diffusion of personal responsibility. 5) Blind obedience to authority. 6) Uncritical conformity to the group’s norms. 7) Passive tolerance of evil, through inaction, or indifference. In hindsight, I can see each one of these points were present in the apple barrel of Scientology that I lived through.   Acknowledgments                     There are numerous people I would like to acknowledge for their support and encouragement during the very difficult task of going back to some dark places in my past to get this book written. They do no want their names used, but they know who they are, and my appreciation is deep and well known to them. I would like to thank Jeferson Hawkins for both his Cover designs and other help along this road. I want to acknowledge Bernice Mennis, Ben Bashore for their personal help over the years. There is much I can say about Vermont College, but the simplest is that they gave me the environment, freedom and courage to study what I needed to write

In an analysis of over one billion pieces of emoji data across the globe, across numerous categories, it wasn’t surprising to find that UK residents had the highest ratio of “winking” emojis, a means, perhaps, of compensating for their usual reserve.1

Risky strategies can be analyzed numerically; uncertain strategies, Ellsberg suggested, were beyond the bounds of formal mathematical analysis

Clustering analysis developed originally from anthropology in 1932, before it was introduced to psychology in 1938 and was later adopted by personality psychology in 1943 for trait theory classification. Today, clustering analysis is used in data mining, information retrieval, machine learning, text mining, web analysis, marketing, medical diagnosis, and numerous other fields.

Continuous variables can take on almost any numeric value and can be meaningfully divided into smaller increments, including fractional and decimal values. You often measure a continuous variable on a scale. For example, when you measure height, weight, and temperature, you have continuous data. Categorical variables have values that you can put into a countable number of distinct groups based on a characteristic. Categorical variables are also called qualitative variables or attribute variables. For example, college major is a categorical variable that can have values such as psychology, political science, engineering, biology, etc.

Even in cases where life is too messy for us to expect a strict numerical analysis or a ready answer, using intuitions and concepts honed on the simpler forms of these problems offers us a way to understand the key issues and make progress.

Let us look at the correlation between temperature, humidity and wind speed and all other features. Since the data also contains categorical features, we cannot only use the Pearson correlation coefficient, which only works if both features are numerical. Instead, I train a linear model to predict, for example, temperature based on one of the other features as input. Then I measure how much variance the other feature in the linear model explains and take the square root. If the other feature was numerical, then the result is equal to the absolute value of the standard Pearson correlation coefficient. But this model-based approach of “variance-explained” (also called ANOVA, which stands for ANalysis Of VAriance) works even if the other feature is categorical. The “variance-explained” measure lies always between 0 (no association) and 1 (temperature can be perfectly predicted from the other feature). We calculate the explained variance of temperature, humidity and wind speed with all the other features. The higher the explained variance (correlation), the more (potential) problems with PD plots. The following figure visualizes how strongly the weather features are correlated with other features.

Despite some scientific debate, numerous studies over the past twenty-plus years have shown that it’s very much possible to be “fat and fit.” For example, a 2017 study of more than five thousand people28 and a 2014 meta-analysis of ten studies with nearly ninety-three thousand participants29 found no increased risk of cardiovascular disease or death for physically active higher-weight people. Additionally, a 2021 review of the evidence found that most cardiometabolic risk factors associated with high body mass index (BMI) can be improved with physical activity independent of weight loss, and that increases in cardiorespiratory fitness or physical activity are consistently associated with greater reductions in mortality risk than is intentional weight loss.

The man in charge of it, Zvi Lanir, sought Danny’s help. In the end, Danny and Lanir conducted an elaborate exercise in decision analysis. Its basic idea was to introduce a new rigor in dealing with questions of national security. “We started with the idea that we should get rid of the usual intelligence report,” said Danny. “Intelligence reports are in the form of essays. And essays have the characteristic that they can be understood any way you damn well please.” In place of the essay, Danny wanted to give Israel’s leaders probabilities, in numerical form.

To demand or preach mechanical precision, even in principle, in a field incapable of it is to be blind and to mislead others,” as the British liberal philosopher Isaiah Berlin noted in an essay on political judgment. Indeed what Berlin says of political judgment applies more broadly: judgment is a sort of skill at grasping the unique particularities of a situation, and it entails a talent for synthesis rather than analysis, “a capacity for taking in the total pattern of a human situation, of the way in which things hang together.”7 A feel for the whole and a sense for the unique are precisely what numerical metrics cannot supply.

Basically, this is a rigorous analysis that shows that numerous universal constants—like the force of gravity, the weight of a proton, the force that binds protons and neutrons within atomic nuclei, and so on—have to be almost exactly what they are for life to exist in the universe. The odds of these constants all having the precise values needed for life are worse than the odds of winning the lottery a thousand times in a row. “So how is this possible? Theologians believe God is the answer. Scientists were initially stumped but soon declared that this riddle was easily answered if one posited an infinite number of universes. Given an infinite number of universes, one of them was bound to get it right. And, lucky for us, we happen to find ourselves in this perfect universe.” Faith raised her eyebrows. “But science admits it has no way to prove the existence of other universes. So both explanations rely on faith. Given this, why is a creator any more absurd than infinite universes? A creator may not be the answer, but science’s answer isn’t really any better.

Qualitative studies of CG lightning suppression through injecting metallic chaff into maturing cumulonimbus also have recently been suggested (Orville, 2001). A few years ago thunderstorms developed in Arizona in which one complex storm produced numerous CG and another almost none. Post analysis found that the CG-free storm complex had formed in an arca where the military had been conducting chafi experiments that same day, and it was postulated that the chaff had suppressed electric fields in the storm. resulting in only in-cloud lightning production. Limited fieldwork has been done on this topic.

Qualitative studies of CG lightning suppression through injecting metallic chaff into maturing cumulonimbus also have recently been suggested (Orville, 2001). A few years ago thunderstorms developed in Arizona in which one complex storm produced numerous CG and another almost none. Post analysis found that the CG-free storm complex had formed in an arca where the military had been conducting chafi experiments that same day, and it was postulated that the chaff had suppressed electric fields in the storm. resulting in only in-cloud lightning production. Limited fieldwork has been done on this topic.

In fact, Odin is not alone in having valkyries in his service. Analysis of the texts and of the attested valkyrie names reveals that these women can be sorted into three major groups: some are indisputably warriors and bear the names of fighters (“Battle,” “Force,” “Paralyzing,” etc.), others have “feminine”-sounding names, and the last group, which is the least numerous, has names associated with fate. 37 The goddess Freya has a right to half of those who die on the battlefield (valr), while the other half are reserved for Odin; furthermore, this goddess is also a swan maiden. I should add that because of the theme of transformation into swans, water is also closely associated with these mythological legends. We are still evolving in the same great complex of representations: elves/water–death–life–Third Function. One final detail we may point out: the valkyries do not shun the love of men (cf. Brynhildr, who disobeys Odin on account of her love for Helgi), and a very ancient belief, which we see crop up more recently in the writings of Paracelsus, is that water sprites are the closest of such elemental spirits to humans and the most apt to form unions with them.

regression as dummy variables Explain the importance of the error term plot Identify assumptions of regression, and know how to test and correct assumption violations Multiple regression is one of the most widely used multivariate statistical techniques for analyzing three or more variables. This chapter uses multiple regression to examine such relationships, and thereby extends the discussion in Chapter 14. The popularity of multiple regression is due largely to the ease with which it takes control variables (or rival hypotheses) into account. In Chapter 10, we discussed briefly how contingency tables can be used for this purpose, but doing so is often a cumbersome and sometimes inconclusive effort. By contrast, multiple regression easily incorporates multiple independent variables. Another reason for its popularity is that it also takes into account nominal independent variables. However, multiple regression is no substitute for bivariate analysis. Indeed, managers or analysts with an interest in a specific bivariate relationship will conduct a bivariate analysis first, before examining whether the relationship is robust in the presence of numerous control variables. And before conducting bivariate analysis, analysts need to conduct univariate analysis to better understand their variables. Thus, multiple regression is usually one of the last steps of analysis. Indeed, multiple regression is often used to test the robustness of bivariate relationships when control variables are taken into account. The flexibility with which multiple regression takes control variables into account comes at a price, though. Regression, like the t-test, is based on numerous assumptions. Regression results cannot be assumed to be robust in the face of assumption violations. Testing of assumptions is always part of multiple regression analysis. Multiple regression is carried out in the following sequence: (1) model specification (that is, identification of dependent and independent variables), (2) testing of regression assumptions, (3) correction of assumption violations, if any, and (4) reporting of the results of the final regression model. This chapter examines these four steps and discusses essential concepts related to simple and multiple regression. Chapters 16 and 17 extend this discussion by examining the use of logistic regression and time series analysis. MODEL SPECIFICATION Multiple regression is an extension of simple regression, but an important difference exists between the two methods: multiple regression aims for full model specification. This means that analysts seek to account for all of the variables that affect the dependent variable; by contrast, simple regression examines the effect of only one independent variable. Philosophically, the phrase identifying the key difference—“all of the variables that affect the dependent variable”—is divided into two parts. The first part involves identifying the variables that are of most (theoretical and practical) relevance in explaining the dependent

Learning a second language entails learning numerous aspects of that language, including vocabulary, grammar, pronunciation, composition, reading, culture, and even body language. Unfortunately, traditionally vocabulary has received less attention in second language (L2) pedagogy than any of these other aspects, particularly grammar. Arguably, vocabulary is perhaps the most important component in L2 ability. For more than 2,000 years, the study of a foreign language primarily entailed grammatical analysis, which was practiced through translation of written work (Hinkel & Fotos, 2002). As a result, vocabulary has been academically excluded from or at best limited within L2 curricula and classroom teaching. A perusal of ESL textbooks quickly reveals a lack of focus on vocabulary. Unlike books in French, Spanish, or other foreign languages, there are no vocabulary lists in the lessons/units or vocabulary index at the back of the book. Exercises practicing vocabulary may be found in reading books, but such exercises are rarely found in grammar books, speaking books, listening books, or writing books in spite of the importance of vocabulary in these areas.

... the development of mathematics, for the sciences and for everybody else, does not often come from pure math. It came from the physicists, engineers, and applied mathematicians. The physicists were on to many ideas which couldn’t be proved, but which they knew to be right, long before the pure mathematicians sanctified it with their seal of approval. Fourier series, Laplace transforms, and delta functions are a few examples where waiting for a rigorous proof of procedure would have stifled progress for a hundred years. The quest for rigor too often meant rigor mortis. The physicists used delta functions early on, but this wasn’t really part of mathematics until the theory of distributions was invoked to make it all rigorous and pure. That was a century later! Scientists and engineers don’t wait for that: they develop what they need when they need it. Of necessity, they invent all sorts of approximate, ad hoc methods: perturbation theory, singular perturbation theory, renormalization, numerical calculations and methods, Fourier analysis, etc. The mathematics that went into this all came from the applied side, from the scientists who wanted to understand physical phenomena. [...] So much of mathematics originates from applications and scientific phenomena. But we have nature as the final arbiter. Does a result agree with experiment? If it doesn’t agree with experiment, something is wrong.

every major discussion of ethics these days begins with an analysis of the chaotic situation of modern culture. Even secular writers and thinkers are calling for some sort of basic agreement on ethical behavior. Humanity’s “margin of error,” they say, is shrinking with each new day. Our survival is at stake. These “prophets of doom” point out that man’s destructive capability increased from 1945 to 1960 by the same ratio as it did from the primitive weapons of the Stone Age to the dropping of the atomic bomb on Hiroshima. The thawing of the Cold War provided little comfort. Numerous nations have nuclear arms now or are close to having them. What, besides

Most of the recent literature on creativity (Csikszentmihalyi, 1988, 2000; Gruber & Wallace, 2000; Sternberg & Lubart, 1996) suggests that creativity is the result of a confluence of one or more of the factors from these six aforementioned categories. The “confluence” approach to the study of creativity has gained credibility, and the research literature has numerous confluence theories for better understanding the process of creativity. A review of the most commonly cited confluence theories of creativity and a description of the methodology employed for data collection and data analysis in this study follow.

During World War II, the United States manufactured approximately 45 percent of all armaments produced by all parties engaged in the conflict. Scientists and technicians worked at a feverish rate on the design, testing, modification, and analysis of these weapons, and their efforts required extensive numerical calculations. Trained specialists—usually women called “computers”—produced many of the numbers, using desk calculators. The time required to solve a problem this way was often expressed in “girl hours.

The scientific gauge is quantity: space, size, and strength of forces can all be reckoned numerically. The comparable "yardstick" in the traditional hierarchy was quality. It had, over the millennia, two distinct readings that overlapped. To the popular mind it meant essentially euphoria: better meant happier, worse less happy. Reflective minds, on the other hand, considered happiness to be only an aspect of quality, not its defining feature. The word "significance" points us in the direction of the feature they considered fundamental, but significance too was derivative. It was taken for granted that the higher worlds abounded in meaning, significance, and importance, but this was because they were saturated with Being and were therefore more real. *Sat*, *Chit*, *Ananda*: Being, Awareness, and Bliss. All three pertained, but Being, being basic, came first. In the last analysis, the scale in the traditional hierarchy was ontological." —from_The Forgotten Truth_

Sometimes the strength will be less obvious. Consider Charles Darwin's finches, a subject you may vaguely remember from high school biology class. When Darwin first encountered these birds on the Galapagos Islands, he gathered numerous specimens, not quite realizing what he had discovered. Upon his return, he presented these specimens to the famous English ornithologist John Gould for identification. Gould's analysis revealed that the specimens Darwin had submitted were in fact highly variable. What at first glance were all just "finches" turned out to be twelve different species. There were similarities, but evolution had allowed each to develop a distinctive strength. Each species had a novel beak structure that allowed it to exploit a specific food resource. Some evolved to eat seeds, others fruit, others insects, and others grubs. In business terms, they all had similar core competencies (feathers, wings, feet, beak), but it was a distinctive, seemingly subtle strength—the type of beak—that allowed the finches to effectively compete for a specific type of food.

Modern history teaches that organization and numerical strength cannot prevent movements from failing if they don't develop a good analysis of the situation they are facing.

Using this technique, Baum et al constructed a forest that contained 1,000 decision trees and looked at 84 co-variates that may have been influencing patients' response or lack of response to the intensive lifestyle modifications program. These variables included a family history of diabetes, muscle cramps in legs and feet, a history of emphysema, kidney disease, amputation, dry skin, loud snoring, marital status, social functioning, hemoglobin A1c, self-reported health, and numerous other characteristics that researchers rarely if ever consider when doing a subgroup analysis. The random forest analysis also allowed the investigators to look at how numerous variables *interact* in multiple combinations to impact clinical outcomes. The Look AHEAD subgroup analyses looked at only 3 possible variables and only one at a time. In the final analysis, Baum et al. discovered that intensive lifestyle modification averted cardiovascular events for two subgroups, patients with HbA1c 6.8% or higher (poorly managed diabetes) and patients with well-controlled diabetes (Hba1c < 6.8%) and good self-reported health. That finding applied to 85% of the entire patient population studied. On the other hand, the remaining 15% who had controlled diabetes but poor self-reported general health responded negatively to the lifestyle modification regimen. The negative and positive responders cancelled each other out in the initial statistical analysis, falsely concluding that lifestyle modification was useless. The Baum et al. re-analysis lends further support to the belief that a one-size-fits-all approach to medicine is inadequate to address all the individualistic responses that patients have to treatment. 

Assassination of John F. Kennedy Neil recalls that when John F. Kennedy returned home from his last meeting with President Sukarno in Indonesia relating to efforts to establish a new US financial system – at that time, JFK already had two strikes against him. Firstly, Kennedy returned West Papua from the Dutch to the Indonesians; thereby alienating Big Oil and corporate magnates that had significant control over strategic locations also known for their gold deposits. Secondly, Kennedy overlooked the deception with regards to his very own Vice President, Lyndon Johnson who was receiving all the information relating to the proceedings in Indonesia that he was forwarding to his cabal handlers, including the dissolution of both the CIA and the Federal Reserve Banks. This directly led to John F. Kennedy’s assassination in 1963. - Both Presidents Kennedy and Sukarno were working on numerous projects to make their nations stronger and greater; but one such project in particular was the new American financial system; eliminating all privately-owned Federal Reserve and Central Bank FIAT currency printing – and returning the power of issuance of the nation’s currency to the government itself. 406

A popular misconception is that decision analysis is unemotional, dehumanizing, and obsessive because it uses numbers and arithmetic in order to guide important life decisions. Isn’t this turning over important human decisions “to a machine,” sometimes literally a computer — which now picks our quarterbacks, our chief executive officers, and even our lovers? Aren’t the “mathematicizers” of life, who admittedly have done well in the basic sciences, moving into a context where such uses of numbers are irrelevant and irreverent? Don’t we suffer enough from the tyranny of numbers when our opportunities in life are controlled by numerical scores on aptitude tests and numbers entered on rating forms by interviewers and supervisors? In short, isn’t the human spirit better expressed by intuitive choices than by analytic number crunching? Our answer to all these concerns is an unqualified “no.” There is absolutely nothing in the von Neumann and Morgenstern theory — or in this book — that requires the adoption of “inhumanly” stable or easily accessed values. In fact, the whole idea of utility is that it provides a measure of what is truly personally important to individuals reaching decisions. As presented here, the aim of analyzing expected utility is to help us achieve what is really important to us. As James March (1978) points out, one goal in life may be to discover what our values are. That goal might require action that is playful, or even arbitrary. Does such action violate the dictates of either rationality or expected utility theory? No. Upon examination, an individual valuing such an approach will be found to have a utility associated with the existential experimentation that follows from it. All that the decision analyst does is help to make this value explicit so that the individual can understand it and incorporate it into action in a noncontradictory manner.

In a famous analysis, Yale psychologist Irving Janis identified groupthink as the culprit behind numerous American foreign-policy disasters, including the Bay of Pigs invasion and the Vietnam War.

Below the highest stratum in the ruling class there is always, even in autocratic systems, another that is much more numerous and comprises all the capacities for leadership in the country. Without such a class any sort of social organization would not in itself be sufficient or leading and directing the activities of the masses. In the last analysis, therefore, the stability of any political organism depends on the level of morality, intelligence and activity that this second stratum has attained. Any intellectual or moral deficiencies in this second stratum, accordingly, represent a graver danger to the political structure, and one that is harder to repair, than the presence of similar deficiencies in the few dozen persons who control the workings of the state machine.

The idea that society can be made more consistent, more accurate, and more fair by replacing idiosyncratic human judgment with numerical models is hardly a new one. In fact, their use even in criminal justice is nearly a century old.

Buried within the canon of philosophy are the histories of numerous other philosophies, repressed systems of thought that sometimes emerge like cerebral ghosts to haunt the rational, daylight world of the lumen naturale. Plato’s transmigration of souls, Descartes’ pineal gland, Berkeley’s tar water, Nietzsche’s eternal return—these are the notions that embarrass philosophy, that are explained away with reference to ignorance of the times or idiosyncrasies of the thinker. But sometimes these cryptophilosophies refuse to go away: they appear again and again, in the work of thinker after thinker, a mass hallucination that occurs not in a crowd in space but in a series over time. Such is the case of exophilosophy. What is it? Like its peer exobiology, exophilosophy is the study of life beyond earth—specifically the philosophical study of life beyond earth. In the broadest sense its objects include all theological entities (gods and angels and demons as extraterrestrial life forms) and the thousand other alien figures that populate philosophy: the daemon of Socrates, the Übermensch of Nietzsche, the Other of phenomenology. Not only advocacy but also the critical analysis of supramundane entities pertains as well, and thus the ghosts scorned by Spinoza and the spiritualists exposed by Schopenhauer also take their rightful place in the history of exophilosophy.

The ‘quantitative revolution’ in geography required the discipline to adopt an explicitly scientific approach, including numerical and statistical methods, and mathematical modelling, so ‘numeracy’ became another necessary skill. Its immediate impact was greatest on human geography as physical geographers were already using these methods. A new lexicon encompassing the language of statistics and its array of techniques entered geography as a whole. Terms such as random sampling, correlation, regression, tests of statistical significance, probability, multivariate analysis, and simulation became part both of research and undergraduate teaching. Correlation and regression are procedures to measure the strength and form, respectively, of the relationships between two or more sets of variables. Significance tests measure the confidence that can be placed in those relationships. Multivariate methods enable the analysis of many variables or factors simultaneously – an appropriate approach for many complex geographical data sets. Simulation is often linked to probability and is a set of techniques capable of extrapolating or projecting future trends.

Below the highest stratum in the ruling class there is always, even in autocratic systems, another that is much more numerous and comprises all the capacities for leadership in the country. Without such a class any sort of social organization would be impossible. The higher stratum would not in itself be sufficient or leading and directing the activities of the masses. In the last analysis, therefore, the stability of any political organism depends on the level of morality, intelligence and activity that this second stratum has attained […] Any intellectual or moral deficiencies in this second stratum, accordingly, represent a graver danger to the political structure, and one that is harder to repair, than the presence of similar deficiencies in the few dozen persons who control the workings of the state machine.21

For a scientist, the only valid question is to decide whether the phenomenon can be studied by itself, or whether it is an instance of a deeper problem. This book attempts to illustrate, and only to illustrate, the latter approach. And my conclusion is that, through the UFO phenomenon, we have the unique opportunities to observe folklore in the making and to gather scientific material at the deepest source of human imagination. We will be the object of much contempt by future students of our civilization if we allow this material to be lost, for "tradition is a meteor which, once it falls, cannot be rekindled." If we decide to avoid extreme speculation, but make certain basic observations from the existing data, five principal facts stand out rather clearly from our analysis so far: Fact 1. There has been among the public, in all countries, since the middle of 1946, an extremely active generation of colorful rumors. They center on a considerable number of observations of unknown machines close to the ground in rural areas, the physical traces left by these machines, and their various effects on humans and animals. Fact 2. When the underlying archetypes are extracted from these rumors, the extraterrestrial myth is seen to coincide to a remarkable degree with the fairy-faith of Celtic countries, the observations of the scholars of past ages, and the widespread belief among all peoples concerning entities whose physical and psychological description place them in the same category as the present-day ufonauts. Fact 3. The entities human witnesses report to have seen, heard, and touched fall into various biological types. Among them are beings of giant stature, men indistinguishable from us, winged creatures, and various types of monsters. Most of the so-called pilots, however, are dwarfs and form two main groups: (1) dark, hairy beings – identical to the gnomes of medieval theory – with small, bright eyes and deep, rugged, "old" voices; and (2) beings – who answer the description of the sylphs of the Middle Ages or the elves of the fairy-faith – with human complexions, oversized heads, and silvery voices. All the beings have been described with and without breathing apparatus. Beings of various categories have been reported together. The overwhelming majority are humanoid. Fact 4. The entities' reported behavior is as consistently absurd as the appearance of their craft is ludicrous. In numerous instances of verbal communications with them, their assertions have been systematically misleading. This is true for all cases on record, from encounters with the Gentry in the British Isles to conversations with airship engineers during the 1897 Midwest flap and discussions with the alleged Martians in Europe, North and South America, and elsewhere. This absurd behavior has had the effect of keeping professional scientists away from the area where that activity was taking place. It has also served to give the saucer myth its religious and mystical overtones. Fact 5. The mechanism of the apparitions, in legendary, historical, and modern times, is standard and follows the model of religious miracles. Several cases, which bear the official stamp of the Catholic Church (such as those in Fatima and Guadalupe), are in fact – if one applies the deffinitions strictly – nothing more than UFO phenomena where the entity has delivered a message having to do with religious beliefs rather than with space or engineering.

Beyond the storage and analysis capabilities of a machine built to emotionlessly evaluate a choice on the basis of abstract psychological data reduced to a simple numerical formula, the charismatic power of a nickname had just cast the decisive vote in a decision that was going to upend the lives of numerous human beings. According to that same report, the incident that stood at the origin of that nickname had occurred in Chad, in an extreme life or death situation. But no board of inquiry had managed to rule on any sort of recurring propensity for cannibalism.

Given the finite and nondeterministic nature of these observations, the estimate of the covariance matrix includes some amount of noise. Empirical covariance matrices derived from estimated factors are also numerically ill-conditioned, because those factors are also estimated from flawed data. Unless we treat this noise, it will impact the calculations we perform with the covariance matrix, sometimes to the point of rendering the analysis useless.

NAN – ‘not a number’, only applying to numeric vectors. NULL – ‘empty’ value or set. Often returned by expressions where the value is undefined. Inf – value for ‘infinity’ and

From the mid-eighteenth century onward, computers, frequently women, were on the payrolls of corporations, engineering firms, and universities, performing calculations and doing numerical analysis, sometimes with the use of a rudimentary calculator.

Sensitive to the fact that numerous factors besides race can influence the decision making of prosecutors, judges, and juries, Baldus and his colleagues subjected the raw data to highly sophisticated statistical analysis to see if nonracial factors might explain the disparities. Yet even after accounting for thirty-five nonracial variables, the researchers found that defendants charged with killing white victims were 4.3 times more likely to receive a death sentence than defendants charged with killing blacks. Black defendants, like McCleskey, who killed white victims had the highest chance of being sentenced to death in Georgia.53

In chess one realises that all education is ultimately self education. This idea is a timely consideration in our data driven world. Chess lends itself to structural information and quantitive analysis in a range of ways. For instance the numerical value of the pieces, databases of millions of games, computerised evaluation functions and the international rating system. However, the value of the experience of playing the game is more qualitative than quantitive. Like any competitive pursuit or sport, chess is an elaborate pretext for the production of stories. The benign conceit of rules and points and tournaments generates a narrative experience in which you are at once co-director, actor and spectator. Chess is education in the literal sense of bringing forth, and it is self education because our stories about a game emerge as we play it, as we try to achieve our goals, just as they do in real life. Chess stories are of our own making and they are often about challenges we overcame or failed to overcome. Every chess player knows the experience of encountering a vexed colleague whose desperate to share their tragic tale in which they were “completely winning!” until they screwed up and lost. And yet we also know tougher characters who recognise that taking resolute responsibility for your mistakes, no matter how painful, is the way to grow as a person and a player. As the child psychologist Bruno Bettelheim says: "we grow, we find meaning in life and security in ourselves by having understood and solved personal problems on our own, not by having them explained to us by others”.

In an impact analysis, the impact can be expressed as a rating such as H-M-L (High-Medium-Low) or as a numeric scale, and it can also be expressed in financial terms.

more interesting is the process by which a young man's parents, who purportedly love him, can be induced to send him off to war to his death. Although the scope of this work will not allow this matter to be expanded in full detail, nevertheless, a coarse overview will be possible and can serve to reveal those factors which must be included in some numerical form in a computer analysis of social and war systems.

The organizational consequence of this highly quantitative image of defense decision-making is an independent and high-level office of systems analysis (or program analysis) reporting directly to the secretary. This office, separated from the parochialism of the individual services, commands, and functional offices of the Defense Department, is charged with de novo analysis of the services' program proposals (and, indeed, with the generation of alternative programs) to assess the relative merits of different potential uses of the same dollars. Its activities culminate in the secretary's decision on a single coherent set of numerically defined programs. This model imposes a requirement for close interaction between the secretary of defense and the principal program analyst. A suitable person for the job is difficult to obtain without granting him or her direct access to the secretary. This model, therefore, requires that the chief program analyst report directly to the secretary and it inevitably limits the program and budget role of the other chief officials of the OSD, especially the principal policy adviser. The model leaves unresolved how the guidance for the analysis process is to be developed and even how choices are to be made. Analysis is not always made rigorous and objective simply by making it quantitative, and not everything relevant can be quantified. At its extreme, it can degenerate into a system in which objectives become important because they can be quantified, rather than quantification being important because it can illuminate objectives.

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