On Randomness VIII (Events II)

"Our lives today are not conducted in linear terms. They are much more quantified; a stream of random events is taking place." (James G Ballard, [Conversation with George MacBeth on Third Programme - BBC], 1967)

"Events may appear to us to be random, but this could be attributed to human ignorance about the details of the processes involved." (Brain S Everitt, "Chance Rules", 1999)

"That randomness gives rise to innovation and diversity in nature is echoed by the notion that chance is also the source of invention in the arts and everyday affairs in which naturally occurring processes are balanced between tight organization, where redundancy is paramount, and volatility, in which little order is possible. One can argue that there is a difference in kind between the unconscious, and sometimes conscious, choices made by a writer or artist in creating a string of words or musical notes and the accidental succession of events taking place in the natural world. However, it is the perception of ambiguity in a string that matters, and not the process that generated it, whether it be man-made or from nature at large." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"The subject of probability begins by assuming that some mechanism of uncertainty is at work giving rise to what is called randomness, but it is not necessary to distinguish between chance that occurs because of some hidden order that may exist and chance that is the result of blind lawlessness. This mechanism, figuratively speaking, churns out a succession of events, each individually unpredictable, or it conspires to produce an unforeseeable outcome each time a large ensemble of possibilities is sampled."  (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"Random events often come like the raisins in a box of cereal - in groups, streaks, and clusters. And although Fortune is fair in potentialities, she is not fair in outcomes." (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"The outline of our lives, like the candles flame, is continuously coaxed in new directions by a variety of random events that, along with our responses to them, determine our fate." (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"Why is the human need to be in control relevant to a discussion of random patterns? Because if events are random, we are not in control, and if we are in control of events, they are not random. There is therefore a fundamental clash between our need to feel we are in control and our ability to recognize randomness. That clash is one of the principal reasons we misinterpret random events."  (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"Quantum physicists today are reconciled to randomness at the individual event level, but to expect causality to underlie statistical quantum phenomena is reasonable. Suppose a person shakes an ink pen such that ink spots are formed on a white wall, in what appears for all intents and purposes, randomly. Let us further suppose the random ink spots accumulate to form precise pictures of different known persons' faces every time. We will not regard the overall result to be a happenchance; we are apt to suspect there must be a 'method' to the person who is shaking the ink pen." (Ravi Gomatam) [response to Nobel Laureate Steven Weinberg's article "Einstein's Mistakes", Physics Today Vol. 59 (4), 2005]

"We are hardwired to make sense of the world around us - to notice patterns and invent theories to explain these patterns. We underestimate how easily pat - terns can be created by inexplicable random events - by good luck and bad luck." (Gary Smith, "Standard Deviations", 2014)

From Parts to Wholes (Unsourced)

"By the word symmetry […] one thinks of an external relationship between pleasing parts of a whole; mostly the word is used to refer to parts arranged regularly against one another around a centre. We have […] observed [these parts] one after the other, not always like following like, but rather a raising up from below, a strength out of weakness, a beauty out of ordinariness." (Johann Wolfgang von Goethe)

"Every part is disposed to unite with the whole, that it may thereby escape from its own incompleteness." (Leonardo Da Vinci)

"If nature leads to mathematical forms of great simplicity and beauty - to forms that no one has previously encountered - we cannot help thinking that they are true and that they revealed genuine features of Nature." (Werner K Heisenberg)

"There is a fundamental error in separating the parts from the whole, the mistake of atomizing what should not be atomized. Unity and complementarity constitute reality." (Werner Heisenberg)

"The part always has a tendency to reunite with its whole in order to escape from its imperfection." (Leonardo Da Vinci)

"The whole is simpler than its parts." (Josiah W Gibbs)

"Whatever Nature undertakes, she can only accomplish it in a sequence. She never makes a leap. For example she could not produce a horse if it were not preceded by all the other animals on which she ascends to the horse’s structure as if on the rungs of a ladder. Thus every one thing exists for the sake of all things and all for the sake of one; for the one is of course the all as well. Nature, despite her seeming diversity, is always a unity, a whole; and thus, when she manifests herself in any part of that whole, the rest must serve as a basis for that particular manifestation, and the latter must have a relationship to the rest of the system." (Johann Wolfgang von Goethe)

On Diversity (2000-)

"Diversity and independence are important because the best collective decisions are the product of disagreement and contest, not consensus or compromise." (James Surowiecki, "The Wisdom of Crowds", 2005)

"The fact that cognitive diversity matters does not mean that if you assemble a group of diverse but thoroughly uninformed people, their collective wisdom will be smarter than an expert's. But if you can assemble a diverse group of people who possess varying degrees of knowledge and insight, you're better off entrusting it with major decisions rather than leaving them in the hands of one or two people, no matter how smart those people are." (James Surowiecki, "The Wisdom of Crowds", 2005)

"Learning emerges from discovery, not directives; reflection, not rules; possibilities, not prescriptions; diversity, not dogma; creativity and curiosity, not conformity and certainty; and meaning, not mandates." (Stephanie P Marshall, "The Power to Transform: Leadership That Brings Learning and Schooling to Life", 2006)

"By interlinking causes, by searching always for unity in the face of superficial diversity, modern scientific explanations prize depth above breadth. A deep and narrow theory can, and often does, graduate to become a deep and broad one. A broad and shallow theory never does." (John D Barrow, "New Theories of Everything", 2007)

"[...] diverse, connected, interdependent entities whose behavior is determined by rules, which may adapt, but need not. The interactions of these entities often produce phenomena that are more than the parts. These phenomena are called emergent." (Scott E Page, "Diversity and Complexity", 2010)

"If we can understand how to leverage diversity to achieve better performance and greater robustness, we might anticipate and prevent collapses." (Scott E Page, "Diversity and Complexity", 2010)

On Diversity (1900-1999)

"What is a philosophy? It Is an answer satisfactory to the reason to all the great problems of life. That is what is meant by philosophy. It must satisfy the reason, and it must show the unity underlying the endless diversity of the facts that science observes." (Annie Besant, "The Immediate Future", 1911)

"Science is reduction. Mathematics is its ideal, its form par excellence, for it is in mathematics that assimilation, identification, is most perfectly realized. The universe, scientifically explained, would be a certain formula, one and eternal, regarded as the equivalent of the entire diversity and movement of things." (Émile Boutroux, "Natural law in Science and Philosophy", 1914)

"The world is an endless variety of facts, linked together by necessary and immutable bonds." (Émile Boutroux, "Natural law in Science and Philosophy", 1914)

"We must face life as it is and understand that diversity is its most essential feature." (Mary P Follett, "Creative Experience", 1924)

"Science is the attempt to make the chaotic diversity of our sense experience correspond to a logically uniform system of thought." (Albert Einstein, "Considerations Concerning the Fundaments of Theoretical Physics", Science Vol. 91 (2369), 1940)

"Any system that insulates itself from diversity in the environment tends to atrophy and lose its complexity and distinctive nature." (Gareth Morgan, "Images of Organization", 1986)

"The principle of maximum diversity operates both at the physical and at the mental level. It says that the laws of nature and the initial conditions are such as to make the universe as interesting as possible.  As a result, life is possible but not too easy. Always when things are dull, something new turns up to challenge us and to stop us from settling into a rut. Examples of things which make life difficult are all around us: comet impacts, ice ages, weapons, plagues, nuclear fission, computers, sex, sin and death.  Not all challenges can be overcome, and so we have tragedy. Maximum diversity often leads to maximum stress. In the end we survive, but only by the skin of our teeth." (Freeman J Dyson, "Infinite in All Directions", 1988)

"The goal of science is to make sense of the diversity of Nature." (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

"The most wonderful mystery of life may well be the means by which it created so much diversity from so little physical matter." (E. O. Wilson, "The Diversity of Life", 1992)

On Diversity (-1899)

"There never was in the world two opinions alike, no more than two hairs or two grains; the most universal quality is diversity." (Michel de Montaigne, "Essais", 1595)

"The diversity of the phenomena of Nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment." (Johannes Kepler, "Mysterium Cosmographicum", 1596)

"Blind metaphysical necessity, which is certainly the same always and every where, could produce no variety of things. All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being, necessarily existing." (Isaac Newton, "Philosophiæ Naturalis Principia Mathematica", 1687)

"Entium varietates non temere esse minuendas."
"The variety of entities should not be rashly diminished" (Immanuel Kant, "Critique of Pure Reason", 1781)

"As long as men inquire, they will find opportunities to know more upon these topics than those who have gone before them, so inexhaustibly rich is nature in the innermost diversity of her treasures of beauty, order, and intelligence." (J Louis R Agassiz, "Essay on Classification", 1859)

"Unity of plan everywhere lies hidden under the mask of diversity of structure - the complex is everywhere evolved out of the simple." (Thomas H Huxley, "A Lobster; or, the Study of Zoology", 1861)

"The simplicity of nature which we at present grasp is really the result of infinite complexity; and that below the uniformity there underlies a diversity whose depths we have not yet probed, and whose secret places are still beyond our reach." (William Spottiswoode, [Report of the Forty-eighth Meeting of the British Association for the, Advancement of Science] 1878)
 
"Number is but another name for diversity." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)

"Science arises from the discovery of Identity amidst Diversity." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)

"Nature considered rationally, that is to say, submitted to the process of thought, is a unity in diversity of phenomena; a harmony, blending together all created things, however dissimilar in form and attributes; one great whole animated by the breath of life." (Alexander von Humboldt)