The Laws of Adversity

17. září 2004 42 ze 412 4 THE LAWS OF THE FIFTH DISCIPLINE 1 1. Today's problems come from yesterday's "solutions." Once there was a rug merchant who saw that his most beautiful carpet had a large bump in its center. 2 He stepped on the bump to flatten it out—and succeeded. But the bump reappeared in a new spot not far away. He jumped on the bump again, and it disappeared —for a moment, until it emerged once more in a new place. Again and again he jumped, scuffing and mangling the rug in his frustration; until finally he lifted one corner of the carpet and an angry snake slithered out. Often we are puzzled by the causes of our problems; when we merely need to look at our own solutions to other problems in the past. A well-established firm may find that this quarter's sales are off sharply. Why? Because the highly successful rebate program last quarter led many customers to buy then rather than now. Or a new manager attacks chronically high inventory costs and "solves" the problem—except that the salesforce is now spending 20 percent more time responding to angry complaints from customers who are 17. září 2004 43 ze 412 still waiting for late shipments, and the rest of its time trying to convince prospective customers that they can have "any color they want so long as it's black." Police enforcement officials will recognize their own version of this law: arresting narcotics dealers on Thirtieth Street, they find that they have simply transferred the crime center to Fortieth Street. Or, even more insidiously, they learn that a new citywide outbreak of drug-related crime is the result of federal officials intercepting a large shipment of narcotics—which reduced the drug supply, drove up the price, and caused more crime by addicts desperate to maintain their habit. Solutions that merely shift problems from one part of a system to another often go undetected because, unlike the rug merchant, those who "solved" the first problem are different from those who inherit the new problem. 2. The harder you push, the harder the system pushes back. In George Orwell's Animal Farm, the horse Boxer always had the same answer to any difficulty: "I will work harder," he said. At first, his well-intentioned diligence inspired everyone, but gradually, his hard work began to backfire in subtle ways. The harder he worked, the more work there was to do. What he didn't know was that the pigs who managed the farm were actually manipulating them all for their own profit. Boxer's diligence actually helped to keep the other animals from seeing what the pigs were doing. 3 Systems thinking has a name for this phenomenon: "Compensating feedback": when well-intentioned interventions call forth responses from the system that offset the benefits of the intervention. We all know what it feels like to be facing compensating feedback—the harder you push, the harder the system pushes back; the more effort you expend trying to improve matters, the more effort seems to be required. Examples of compensating feedback are legion. Many of the best intentioned government interventions fall prey to compensating feedback. In the 1960s there were massive programs to build low- income housing and improve job skills in decrepit inner cities in the United States. Many of these cities were even worse off in the 1970s despite the largesse of government aid. Why? One reason was that low-income people migrated from other cities and from rural areas to those The Laws of Adversity The Laws of Adversity Bởi: Joe Tye “Every difficulty in life presents us with an opportunity to turn inward and to invoke our own inner resources The trials we endure can and should introduce us to our strengths.” Sharon Lebell: A Manual for Living: Epictetus – A New Interpretation Adversity has certain laws – and, as with physical laws such as the law of gravity – they apply equally to everyone Understanding the laws of adversity can help you persevere through the inevitable challenges Refusing to believe that they apply to you, that you are somehow exempt because you are a good person, will not change the fact that bad things happen to good people, that adversity can be a life-defining event for better or worse, and what happens to you is less important than how you respond to what happens to you Here are the laws: Law #1: The rain will fall on the just and the unjust, and bad things will happen to good people - including you Understand that adversity will come and be ready to welcome it when it does for the lessons it will bring, for the strength and wisdom you will gain from it, and for the people it can bring into your life Law #2: You must pass through the valley of the shadow, but you don’t have to take up permanent residence in the cold darkness Life is a motion picture, not a snapshot - your trajectory is more important than your current position Law #3: Whether it’s the best of times or the worst of times is defined by what you choose to see Without the valleys, you won’t appreciate the mountains, and there are millions of others who would loveto have your problems Law #4: One door closes, another door opens There is opportunity hidden in every single adversity if you have the strength and courage to search for it and to pursue it when you’ve found it Law #5: Falling on your face is good for your head We learn and grow more from our setbacks than we from our successes When things aren’t working, it forces you to look at more creative solutions 1/2 The Laws of Adversity Law #6: Surviving adversity is a great way to build self-confidence, and to give you a more positive perspective on future adversity (if we survived that we can survive anything!) Adversity prepares you for bigger challenges and accomplishments in the future Law #7: What you’ve fought hard to gain you’ll fight hard to keep and vice versa - easy come, easy go Law #8: Playing the role of victim or martyr does not prevent adversity or make it go away, but it does make you weaker and diminishes your ability to cope and grow from the experience Law #9: Adversity makes you stronger by helping you connect with others There is something immensely therapeutic about asking for help, even if the help you receive doesn’t really solve your problem Perhaps it’s the therapy of setting aside false pride and self-sufficiency Adversity helps prevent hubris, arrogance, and complacency Law #10: Adversity keeps teaching - it provides great stories for the grandchildren! Your setbacks can, if you’re committed to learning from them and teaching about them, be the source of great learning for others And the ultimate law of adversity: Every great accomplishment was once the “impossible” dream of a dreamer who refused to quit when the going got tough 2/2 [...]... sense, to each of the other members xviii Preface To mathematicians (at least to most of them, as far as I can make out), mathematics is not just a cultural activity that we have ourselves created, but it has a life of its own, and much of it Wnds an amazing harmony with the physical universe We cannot get any deep understanding of the laws that govern the physical world without entering the world of mathematics... clearly recall how the matter was Wnally resolved, but with the hindsight gained from my much later experiences as a mathematics undergraduate, I guess my schoolteacher was making a brave attempt at telling us the deWnition of a fraction in terms of the ubiquitous mathematical notion of an equivalence class What is this notion? How can it be applied in the case of a fraction and tell us what a fraction... noticed There is, indeed, a profound issue that one comes up against again and again in mathematics and in mathematical physics, which one Wrst encounters in the seemingly innocent operation of cancelling a common factor from the numerator and denominator of an ordinary numerical fraction Those for whom the action of cancelling has become second nature, because of repeated familiarity with such operations,... readership that this will entail I have thought seriously about this question, and have come to the conclusion that what I have to say cannot reasonably be conveyed without a certain amount of mathematical notation and the exploration of genuine mathematical concepts The understanding that we have of the principles that actually underlie the behaviour of our physical world indeed depends upon some appreciation... conveying the idea—and the beauty and the magic—inherent in many important mathematical notions The idea of a fraction such as 3 is simply that it is some kind of an entity which has the 8 property that, when added to itself 8 times in all, gives 3 The magic is that the idea of a fraction actually works despite the fact that we do not really directly experience things in the physical world that are exactly... imprecise physical situations to which the precise mathematical notion of a fraction was to be applied; they did not tell us what that clear-cut mathematical notion actually is Other suggestions came forward, such as 3 is ‘something with [...]... signal the coming end of the collection and to emphasize the final topic of festivals and cult (23:14–19) The placement of sections of apodictic law around the casuistic laws of 21:2–22:19 was done in imitation of the overall A-B-A structure of LH (prologue/casuistic laws/ epilogue) The theme of cultic activity that pervades the prologue helped determine the cultic theme of the initial apodictic laws, ... casuistic laws have close associations with the central casuistic laws of LH (LH 1–282), and CC’s outer apodictic laws have close thematic associations with the outer sections of LH, its prologue and epilogue, especially one particular section of the epilogue The casuistic laws of CC for their part display the same or nearly the same topical order as the laws in the last half of Hammurabi s collection.18 They... Abbreviations and Special Terminology xiii 1 Introduction: The Basic Thesis and Background 3 Part I: Primary Evidence for Dependence: Sequential Correspondences and Date 29 2 The Casuistic Laws 31 3 The Apodictic Laws 51 4 Opportunity and Date for the Use of Hammurabi s and Other Cuneiform Laws 91 Part II: The Compositional Logic of the Covenant Code 121 5 Debt-Slavery and the Seduction of a Maiden (Exodus... of the Great Books library of Akkadian scribes, but that this text had no influence on the Covenant Code? A more parsimonious and compelling explanation of the Covenant Code s origins recommends itself, and that is what this study presents The Evidence in Brief The argument of this book requires detailed textual examination of the whole of the Covenant Code in connection with the Laws of Hammurabi and. .. small groups of casuistic laws on specific topics were created A third stage brought together these small groups of laws into intermediate collections, and these were later brought together into the first and basic edition of CC, consisting of casuistic laws Finally, the collection was expanded with the apodictic laws and incorporated into the narrative According to Jackson’s model, the laws grew up... early dating of the Covenant Code is also supported by a relatively early dating of the laws of Deuteronomy If the latter date to the eighth century, for example, then the Covenant Code may be from the ninth or even tenth century BCE In Project Gutenberg’s An Investigation of the Laws of Thought, by George Boole This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.net Title: An Investigation of the Laws of Thought Author: George Boole Release Date: February 16, 2005 [EBook #15114] Language: English Character set encoding: PDF *** START OF THIS PROJECT GUTENBERG EBOOK LAWS OF THOUGHT *** Produced by David Starner, Joshua Hutchinson, David Bowden and the Online Distributed Proofreading Team. i AN INVESTIGATION OF THE LAWS OF THOUGHT, ON WHICH ARE FOUNDED THE MATHEMATICAL THEORIES OF LOGIC AND PROBABILITIES. BY GEORGE BOOLE, LL. D. PROFESSOR OF MATHEMATICS IN QUEEN’S COLLEGE, CORK. ii TO JOHN RYALL, LL.D. VICE-PRESIDENT AND PROFESSOR OF GREEK IN QUEEN’S COLLEGE, CORK, THIS WORK IS INSCRIBED IN TESTIMONY OF FRIENDSHIP AND ESTEEM PREFACE. —— The following work is not a republication of a former treatise by the Author, entitled, “The Mathematical Analysis of Logic.” Its earlier portion is indeed devoted to the same object, and it begins by establishing the same system of fundamental laws, but its metho ds are more general, and its range of applica- tions far wider. It exhibits the results, matured by som e years of study and reflection, of a principle of investigation relating to the intellectual operations, the previous exposition of which was written within a few weeks after its idea had been conceived. That portion of this work which relates to Logic presupposes in its reader a knowledge of the most important terms of the science, as usually treated, and of its general object. On these points there is no better guide than Archbishop Whately’s “Elements of Logic,” or Mr. Thomson’s “Outlines of the Laws of Thought.” To the former of these treatises, the present revival of attention to this class of studies seems in a great measure due. Some acquaintance with the principles of Algebra is also requisite, but it is not necessary that this application should have been carried beyond the solution of simple equations. For the study of those chapters which relate to the theory of probabilities, a somewhat larger knowledge of Algebra is required, and especially of the doctrine of Elimination, and of the solution of Equations containing more than one unknown quantity. Preliminary information upon the subject-matter will be found in the special treatises on Probabilities in “Lardner’s Cabinet C yclopædia,” and the “Library of Useful Knowledge,” the former of these by Professor De Morgan, the latter by Sir John Lubbock; and in an interesting series of Letters translated from the French of M. Quetelet. Other references will be given in the work. On a first perusal the reader may omit at his discretion, Chapters x., xiv., and xix., together with any of the applications which he may deem uninviting or irrelevant. In different parts of the work, and especially in the notes to the concluding chapter, will be found references to various writers, ancient and modern, chiefly designed to Vietnam Journal of Mathematics 33:1 (2005) 55–62 OntheLawsofLargeNumbersforBlockwise Martingale Differences and Blockwise Adapted Sequences Le Van Thanh and Nguyen Van Quang Department of Mathematics, University of Vinh, Vinh, Nghe An, Vietnam Received September 29, 2003 Revised October 5, 2004 Abstract. In this paper we establish the laws of large numbers for blockwise martin- gale differences and for blockwise adapted sequences which are stochastically dominated by a random variable. Some well-known results from the literature are extended. 1. Introduction and Notations Let {F n ,n ≥ 1} be an increasing σ-fields and let {X n ,n ≥ 1} be a sequence of random variables. We recall that the sequence {X n ,n≥ 1} is said to be adapted to {F n ,n ≥ 1} if each X n is measurable with respect to F n . The sequence {X n ,n ≥ 1} is said to be stochastically dominated by a random variable X if there exists a constant C>0 such that P {|X n |≥t}≤CP{|X|≥t} for all nonnegative real numbers t and for all n ≥ 1. Related to the adapted sequences, Hall and Heyde [3] proved the following theorem. Theorem 1.1. (see [3], Theorem 2.19) Let {F n ,n≥ 1} be an increasing σ-fields and {X n ,n ≥ 1} is adapted to {F n ,n ≥ 1}.If{X n ,n ≥ 1} is stochastically dominated by a random variable X with E|X| < ∞,then 1 n n  i=1 (X i − E(X i |F i−1 )) P → 0 as n →∞. (1.1) In the case, when E(|X| log + |X|) < ∞ or X n are independent, the convergence 56 Le Van Thanh and Nguyen Van Quang in (1.1) can be strengthened to a.s. convergence. Moricz [4] introduced the concept of blockwise m-dependence for a sequence of random variables and extended the classical Kolmogorov strong law of large numbers to the blockwise m-dependence case. Later, the strong law of large numbers for arbitrary blockwise independent random variables was also studied by Gaposhkin [1]. He then showed in [2] that some properties of independent sequences of random variables remain satisfied for the sequences consisting of independent blocks. However, the same problem for sequences of blockwise in- dependent and identically distributed random variables and for blockwise mar- tingale differences is not yet studied. The main results of this paper are Theorems 3.1, 3.3. Theorem 3.1 establishes the strong law of large numbers for arbitrary blockwise martingale differences. In Theorem 3.3, we set up the law of large numbers for the so called blockwise adapted sequences which are stochastically dominated by a random variable X. Some well-known results from the literature are extended. Let {ω(n),n ≥ 1} be a strictly increasing sequence of positive integers with ω(1) = 1. For each k ≥ 1, we set Δ k =  ω(k),ω(k +1)  . We recall that a sequence {X i ,i≥ 1} of random variables is blockwise independent with respect to blocks [Δ k ], if for any fixed k, the sequence {X i } i∈Δ k is independent. Now let {F i ,i ≥ 1} be a sequence of σ-fields such that for any fixed k,the sequence {F i ,i ∈ Δ k } is increasing. The sequence {X i ,i ≥ 1} of random vari- ablesissaidtobeblockwise adapted to {F i ,i≥ 1},ifeachX i is measurable with respect to F i . The sequence {X i , F i ,i≥ 1} called a blockwise martingale differ- ence with respect to blocks [Δ k ], if for any fixed k, the sequence {X i , F i } i∈Δ k is a martingale difference. Let N m =min{n|ω(n) ≥ 2 m }, s m = N m+1 − N m +1, ϕ(i)=max k≤m s k if i ∈ [2 m , 2 m+1 ), Δ (m) =[2 m , 2 m+1 ),m≥ 0, Δ (m) k =Δ k ∩ Δ (m) ,m≥ 0,k ≥ 1, p m =min{k :Δ (m) k = ∅}, q m =max{k :Δ (m) k = ∅}. Since ω(N m − 1) < 2 m ,ω(N m ) ≥ 2 m ,ω(N m+1 ) ≥ 2 m+1 for each m ≥ 1, the number of nonempty blocks [Δ (m) k ] is not larger than s m = N m+1 − N m +1. Assume Δ (m) k = ∅,letr (m) k =min{r : r ∈ Δ (m) k }. Throughout this paper, C denotes a unimportant positive constant which is allowed to be changed. 2. Lemmas In the sequel we will need the following lemmas. Laws of Large Numbers for Blockwise Martingale Differences 57 Lemma 2.1. (Doob’s Inequality) If {X i , F i } N i=1 is a ... learning from them and teaching about them, be the source of great learning for others And the ultimate law of adversity: Every great accomplishment was once the “impossible” dream of a dreamer... you connect with others There is something immensely therapeutic about asking for help, even if the help you receive doesn’t really solve your problem Perhaps it’s the therapy of setting aside.. .The Laws of Adversity Law #6: Surviving adversity is a great way to build self-confidence, and to give you a more positive perspective on future adversity (if we survived