On Time: The Arrow of Time

"Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. [...] I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space. (Arthur Eddington, "The Nature of the Physical World", 1928)

"So far as physics is concerned, time's arrow is a property of entropy alone." (Arthur S Eddington, "The Nature of the Physical World", 1928)

"Time goes forward because energy itself is always moving from an available to an unavailable state. Our consciousness is continually recording the entropy change in the world around us. [...] we experience the passage of time by the succession of one event after another. And every time an event occurs anywhere in this world energy is expended and the overall entropy is increased. To say the world is running out of time then, to say the world is running out of usable energy. In the words of Sir Arthur Eddington, 'Entropy is time's arrow'." (Jeremy Rifkin & Ted Howard, "Entropy: A New World View", 1980)

 "The increase of disorder or entropy with time is one example of what is called an arrow of time something that gives a direction to time and distinguishes the past from the future. There are at least three different directions of time. First, there is the thermodynamic arrow of time - the direction of time in which disorder or entropy increases. Second, there is the psychological arrow of time. This is the direction in which we feel time passes - the direction of time in which we remember the past, but not the future. Third, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting." (Stephen W. Hawking, "The Direction of Time", New Scientist 46, 1987)

"At another level, market crashes constitute beautiful examples of events that we would all like to forecast. The arrow of time is inexorably projecting us toward the undetermined future. Predicting the future captures the imagination of all and is perhaps the greatest challenge." (Didier Sornette, "Why Stock Markets Crash: Critical Events in Complex Systems", 2003)

"More generally, thermodynamics shows that there is an irreversible flow of time. Rather than there being time symmetry and indeed a reversibility of time as postulated in classical physics, a clear distinction is drawn between the past and future. An arrow of time results within open systems in the loss of organization and an increase in randomness or disorder over time. This accumulation of disorder or positive entropy results from the Second Law of Thermodynamics." (John Urry, "Global Complexity", 2003)

"The arrow of time, through the defi ning role it plays in everyday life and its intimate link with the origin of the universe, lies at a singular threshold between the reality we experience and the more refi ned reality cutting-edge science seeks to uncover." (Brian Greene, "The Fabric of the Cosmos: Space, Time, and the Texture of Reality", 2004)

"We often wonder why the more complex systems seem to indicate a preferred direction of time, or an arrow of time, whereas their elementary counterparts do not. […] This has to do with the if-then nature of physics questions. Anything we observe involves laws of motion but also particular initial conditions. […] The initial conditions are what make a situation look peculiar when we time reverse it." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"In the elementary equations of the world, the arrow of time appears only where there is heat. The link between time and heat is therefore fundamental: every time a difference is manifested between the past and the future, heat is involved. In every sequence of events that becomes absurd if projected backward, there is something that is heating up." (Carlo Rovelli, "The Order of Time", 2018)

On Numbers (From Fiction to Science-Fiction)

"We know that there is an infinite, and we know not its nature. As we know it to be false that numbers are finite, it is therefore true that there is a numerical infinity. But we know not of what kind; it is untrue that it is even, untrue that it is odd; for the addition of a unit does not change its nature; yet it is a number, and every number is odd or even (this certainly holds of every finite number). Thus, we may quite well know that there is a God without knowing what He is." (Blaise Pascal, "Pensées", 1670)

"One microscopic glittering point; then another; and another, and still another; they are scarcely perceptible, yet they are enormous. This light is a focus; this focus, a star; this star, a sun; this sun, a universe; this universe, nothing. Every number is zero in the presence of the infinite." (Victor Hugo,"The Toilers of the Sea", 1874)

"Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers; the law of revolution is not a social law, but an immeasurably  greater one. It is a cosmic, universal law - like the laws of the conservation of energy and of the dissipation of energy (entropy)." (Yevgeny Zamiatin, ‘‘On Literature, Revolution, Entropy, and Other Matters’’, 1923)

"Words and numbers are of equal value, for, in the cloak of knowledge, one is warp and the other woof. It is no more important to count the sands than it is to name the stars." (Norton Juster, "The Phantom Tollbooth", 1961)

"Why, numbers are the most beautiful and valuable things in the world.’" (Norton Juster, "The Phantom Tollbooth", 1961)

"Science is not a sacred cow - but there are a large number of would-be sacred cowherds busily devoting quantities of time, energy and effort to the task of making it one, so they can be sacred cowherds." (John W. Campbell Jr., "Prologue to Analog", [introduction] 1962)

"Beyond a critical point within a finite space, freedom diminishes as numbers increase. This is as true of humans as it is of gas molecules in a sealed flask. The human question is not how many can possibly survive within the system, but what kind of existence is possible for those who do survive." (Frank Herbert, "Dune", 1965)

"If a book were written all in numbers, it would be true. It would be just. Nothing said in words ever came out quite even. Things in words got twisted and ran together, instead of staying straight and fitting together. But underneath the words, at the center, like the center of the Square, it all came out even. Everything could change, yet nothing would be lost. If you saw the numbers you could see that, the balance, the pattern. You saw the foundations of the world. And they were solid." (Ursula K Le Guin, "The Dispossessed: An Ambiguous Utopia", 1974)

"What do such machines really do? They increase the number of things we can do without thinking. Things we do without thinking - there's the real danger." (Frank Herbert, "God Emperor of Dune", 1984)

John M Bryson - Collected Quotes

"A causal map is a word-and-arrow diagram in which ideas and actions are causally linked with one another through the use of arrows. The arrows indicate how one idea or action leads to another. Causal mapping makesit possible to articulate a large number of ideas and their interconnections in such a way that people can know what to do in an area of concern, how to do it and why, because the arrows indicate the causes and consequences of an idea or action. Causal mapping is therefore a technique for linking strategic thinking and acting, helping make sense of complex problems, and communicating to oneself and others what might be done about them." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"A statement of strategic aims is powerful when it represents the interaction between all of the goals [Strategy]: the goals are seen as a system where each goal helps deliver other high-level goals and may in turn be helped by the delivery of subordinate goals." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal mapping is a simple and useful technique for addressing situations where thinking– as an individual or as a group– matters. A causal map is a word-and-arrow diagram in which ideas and actions are causally linked with one another through the use of arrows. The arrows indicate how one idea or action leads to another. Causal mapping makes it possible to articulate a large number of ideas and their interconnections in such a way that people can know what to do in an area of concern, how to do it and why, because the arrows indicate the causes and consequences of an idea or action." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal mapping is [...] a technique for linking strategic thinking and acting, helping make sense of complex problems, and communicating to oneself and others what might be done about them. With practice, the use of causal mapping can assist you in moving from 'winging it' when thinking matters to a more concrete and rigorous approach that helps you and others achieve success in an easy and far more reliable way" (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal mapping makes it possible to articulate a large number of ideas and their interconnections in such a way that we can better understand an area of concern. Causal mapping also helps us know what to do about the issue, what it would take to do those things, and what we would like to get out of having done so. Causal mapping is therefore a particularly powerful technique for making sense of complex problems, linking strategic thinking and acting, and helping to communicate to others what might or should be done. " (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Linking focuses attention not on topics but on action: what results might be achieved by doing something, and what things needed to be done to make other things happen." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Positive feedback loops are very important. Even when afeedback loop is made up of competencies, because they are self-sustaining they may be very important resources for the future of the business [Strategy]. A positive loop means that each of the competencies in the loop feeds all of the others. When the feedback loop is distinctive, this will be even more important because the distinctiveness is self-sustaining." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"The process of constructing a map thus allows you to reflect on your own thinking, or that of someone else. Mapping helps you become conscious of your reasoning and to understand clearly what another person is thinking. In turn, that consciousness and understanding can help you reaffirm what you think or else change your mind. Shared understanding and mutual agreement also become possible." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"When an individual uses causal mapping to help clarify their own thinking, we call this technique cognitive mapping, because it is related to personal thinking or cognition. When a group maps their own ideas, we call it oval mapping, because we often use oval-shaped cards to record individuals’ ideas so that they can be arranged into a group’s map. Cognitive maps and oval maps can be used to create a strategic plan, because the maps include goals, strategies and actions, just like strategic plans." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"When people question assumptions, the map may clarify what they are. When logic is challenged, the map may help. When people want to know how goals and strategies are linked, the map may show how they are. The map does not make the decisions. Rather, it provides a record that preserves complexity, yet organizes and categorizes that complexity in such a way that people can understand and manage it. And if more mapping needs to be done, the map is there as a base on which to build." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)