On Problem Solving XX: Life

"The difficult problems in life always start off being simple. Great affairs always start off being small." (Lao Tzu, cca 400 BC)

"Man was not born to solve the problems of the universe, but rather to seek to lay bare the heart of the problem and then confine himself within the limits of what is amenable to understanding." (Johann Wolfgang von Goethe, 1825)

"The greatest art, both in teaching and in life itself, consists in transforming the problem into a postulate." (Johann Wolfgang von Goethe, 1928)

"The meaning and design of a problem seem not to lie in its solution, but in our working at it incessantly." (Carl G Jung, "Modern Man in Search of a Soul", 1933)

"The field of consciousness is tiny. It accepts only one problem at a time. Get into a fist fight, put your mind on the strategy of the fight, and you will not feel the other fellow's punches." (Antoine de Saint-Exupéry, "Flight to Arras", 1942)

"Life ultimately means taking the responsibility to find the right answer to its problems and to fulfill the tasks which it constantly sets for each individual." (Viktor E Frankl, "Man's Search for Meaning", 1946)

"We are built to conquer environment, solve problems, achieve goals, and we find no real satisfaction or happiness in life without obstacles to conquer and goals to achieve." (Maxwell Maltz, "Psycho-Cybernetics", 1960)

"The mystery of life isn't a problem to solve, but a reality to experience." (Frank Herbert, "Dune", 1965)

"Sometimes the situation is only a problem because it is looked at in a certain way. Looked at in another way, the right course of action may be so obvious that the problem no longer exists." (Edward de Bono, "The use of lateral thinking", 1967)

"There are problems in this universe for which there are no answers." (Frank Herbert, "Dune Messiah", 1969)

"The easiest way to solve a problem is to deny it exists." (Isaac Asimov, "The Gods Themselves", 1972)

"When a decision is made to cope with the symptoms of a problem, it is generally assumed that the corrective measures will solve the problem itself. They seldom do." (Masanobu Fukuoka, "The One-Straw Revolution", 1975)

"If you go through the world looking for excellence, you will find excellence. If you go through the world looking for problems you will find problems." (Joseph O'Connor & John Seymour, "Introducing Neuro-Linguistic Programming: Psychological Skills for Understanding and Influencing People", 1990)

"Every problem has a solution, although it may not be the outcome that was originally hoped for or expected."  (Alice Hoffman, "Practical Magic", 1995)

"Pain is a relatively objective, physical phenomenon; suffering is our psychological resistance to what happens. Events may create physical pain, but they do not in themselves create suffering. Resistance creates suffering. Stress happens when your mind resists what is... The only problem in your life is your mind's resistance to life as it unfolds." (Dan Millman, "Everyday Enlightenment: The Twelve Gateways to Personal Growth", 1998)

"[...] all problems can be reperceived as challenges, or 'opportunities' to change, grow or learn." (Robert B Dilts, "Sleight of Mouth: The Magic of Conversational Belief Change", 1999)

"All problems are illusions of the mind." (Eckhart Tolle, "Practicing the Power of Now: Essential Teachings, Meditations, and Exercises", 2001)

"We humans have two great problems: the first is knowing when to begin; the second is knowing when to stop." (Paulo Coelho, "The Zahir: A Novel of Obsession", 2005)

"Most problems we face in life, as I have said already, happen in our minds. Furthermore, problems generally exist in our concept of the past and the future. The past and the future don’t exist except in our minds." (Richard Bandler, "Get the Life You Want: The Secrets to Quick and Lasting Life Change with Neuro-Linguistic Programming", 2008)

"One of the most important aspects of what human beings do is build beliefs. Beliefs are what trap most people in their problems. Unless you believe you can get over something, get through something, or get to something, there is little likelihood you will be able to do it. Your beliefs refer to your sense of certainty on some of your thoughts." (Richard Bandler, "Get the Life You Want: The Secrets to Quick and Lasting Life Change with Neuro-Linguistic Programming", 2008)

"When you can take on board new, positive suggestions and disbelieve the old, limiting suggestions, you will be ready to tackle the rest of your problems, especially your fears." (Richard Bandler, "Get the Life You Want: The Secrets to Quick and Lasting Life Change with Neuro-Linguistic Programming", 2008)

"Our most important problems cannot be solved; they must be outgrown." (Wayne Dyer, "Excuses Begone!: How to Change Lifelong, Self-Defeating Thinking Habits", 2009)

"A problem is a difference between things as desired and things as perceived. […] Seen in this way, the problem could be solved either by changing desires or changing perceptions." (Donald C Gause & Gerald M Weinberg, "Are Your Lights On?", 2011)

"As a practical matter, it is impossible to define natural, day-to-day problems in a single, unique, totally unambiguous fashion. On the other hand, without some common understanding of the problem, a solution will almost invariably be to the wrong problem." (Donald C Gause & Gerald M Weinberg, "Are Your Lights On?", 2011)

"The really important thing in dealing with problems is to know that the question is never answered, but that it doesn't matter, as long as you keep asking. It's only when you fool yourself into thinking you have the final problem definition - the final, true answer - that you can be fooled into thinking you have the final solution. And if you think that, you're always wrong, because there is no such thing as a 'final solution'." (Donald C Gause & Gerald M Weinberg, "Are Your Lights On?", 2011)

Misquoted: Cicero on Probability is the Very Guide of Life

The "probability is the very guide of life" adage is attributed to Joseph Butler (1692-1752) and surprisingly (see [6]) Marcus Tullius Cicero (106-43 BC). Surprisingly because at first glance it is hard to believe that a concept relatively new as the one of probability was known to the antics, even if philosophical texts on divinity, fate, divination, causality or similar topics approached notions like chance or plausibility. 

The concept of probability entered in common usage only starting with 14th century via the French vocabulary, the term being derived directly from the Latin probabilitatem/probabilitas which belong to the family of words derived from 'probabilis' and translated as 'probable' or 'plausible'. 

Cicero used indeed 'probable' (Latin: probabilis) close to its actual meaning and provides a definition for it in "De Inventione" (cca. 91 and 88 BC), one of his earliest works, considered by historians as one of the main works on rhetoric:

"That is probable which for the most part usually comes to pass, or which is a part of the ordinary beliefs of mankind, or which contains in itself some resemblance to these qualities, whether such resemblance be true or false." [1]

Cicero used 'probable' also in "De Natura Deorum" (cca. 45 BC) with the same meaning:

"For we are not people who believe that there is nothing whatever which is true; but we say that some falsehoods are so blended with all truths, and have so great a resemblance to them, that there is no certain rule for judging of, or assenting to propositions; from which this maxim also follows, that many things are probable, which, though they are not evident to the senses, have still so persuasive and beautiful an aspect, that a wise man chooses to direct his conduct by them." [2]

"But, as it is the peculiar property of the Academy to interpose no personal judgment of its own, but to admit those opinions which appear most probable, to compare arguments, and to set forth all that may be reasonably stated in favour of each proposition; and so, without putting forth any authority of its own, to leave the judgment of the hearers free and unprejudiced; we will retain this custom, which has been handed down from Socrates; and this method, dear brother Quintus, if you please, we will adopt as often as possible in all our dialogues together." [2]

However, from 'probable' to 'probability' (Latin: probabilitas) there's an important leap of meaning. The use of 'probability' can be explained by translator's choice of using it in the detriment of terms like 'chance', 'odds' or 'possible', though searches in the online texts of the book in the translations of Charles D Yonge (1878) and Francis Brooks (1896) provided no proximate occurrences of the adage. 

Even more surprising, a similar form of the adage appears in Sextus Empiricus' "Outlines of Pyrrhonism"  (cca. 3rd century):

"Furthermore, as regards the End (the aim of life) we differ from the New Academy; for whereas the men who profess to conform to its doctrine use probability as the guide of life; we live in an undogmatic way by following the laws, customs, and natural affections." [3]

Do we have here another situation in which the translator assumed a choice of words or maybe in the original text there were indeed references to probability? Unfortunately, the available translation used as source for the quote is from Greek. 

The adage in its quoted form can be found in Joseph Butler's "The Analogy of Religion" (1736):

"Probable evidence, in its very nature, affords but an imperfect kind of information, and is to be considered as relative only to beings of limited capacities. For nothing which is the possible object of knowledge, whether past, present, or future, can be probable to an infinite Intelligence; since it cannot but be discerned absolutely as it is in itself, certainly true, or certainly false. To us, probability is the very guide of life." [4]

According to Butler we use probability to guide us in life when we deal with incomplete (imperfect) information, when we can't discern whether things are false or true and/or nuances of grey exist in between. For Cicero the things more probable tend to happen even if the senses can't discern which of the things are more probable, the wisdom of a person relying in the ability in identifying and evaluating the things probable. One can recognize in Cicero’s definition an early glimpse of entropy – the movement toward more probable states.

Despite the deep role propabilities play in life, we can still question adage's generalization - the degree to which we use probabilities to guide us in life. We do occasionally think in terms of the probabilities for an event to happen; we do tend to believe that what is more probable to happen will happen. Probably, the more we are caught in scientific endeavors, the more likely we use probabilities in decision making. Though, there's a limit to it, limit associated to the degree we are able to understand and use probabilities. 

I'd like to believe that Cicero's thoughts were in the proximate range of meaning associated with the early concept of probability, though a deeper analysis of the original text is needed and even then we can only advance suppositions.

Previous Post <<||>> Next Post

References:
[1] Marcus Tullius Cicero (cca. 91 and 88 BC) "De inventione", ["On Invention"]
[2] Marcus Tullius Cicero (45 BC) "De Natura Deorum" ["On the Nature of the Gods"]
[3] Sextus Empiricus (cca. 3rd century) "Outlines of Pyrrhonism"
[4] Joseph Butler (1736) "The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature"
[5] Stanford Encyclopedia of Philosophy (2014) Probability in Medieval and Renaissance Philosophy [source]
[6] Kate L Roberts (1922) Hoyt's New Cyclopedia Of Practical Quotations

On Continuity XI (Life)

"[…] to the scientific mind the living and the non-living form one continuous series of systems of differing degrees of complexity […], while to the philosophic mind the whole universe, itself perhaps an organism, is composed of a vast number of interlacing organisms of all sizes." (James G Needham, "Developments in Philosophy of Biology", Quarterly Review of Biology Vol. 3 (1), 1928)

"[A living organism] feeds upon negative entropy […] Thus, the device by which an organism maintains itself stationary at a fairly high level of orderliness really consists in continually sucking orderliness from its environment." (Erwin Schrodinger, "What is Life? The Physical Aspect of the Living Cell", 1944)

"Every process, event, happening – call it what you will; in a word, everything that is going on in Nature means an increase of the entropy of the part of the world where it is going on. Thus a living organism continually increases its entropy – or, as you may say, produces positive entropy – and thus tends to approach the dangerous state of maximum entropy, which is death. It can only keep aloof from it, i.e. alive, by continually drawing from its environment negative entropy – which is something very positive as we shall immediately see. What an organism feeds upon is negative entropy. Or, to put it less paradoxically, the essential thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while alive." (Erwin Schrödinger, "What is Life?", 1944)

"Hence the awkward expression ‘negative entropy’ can be replaced by a better one: entropy, taken with the negative sign, is itself a measure of order. Thus the device by which an organism maintains itself stationary at a fairly high level of orderliness ( = fairly low level of entropy) really consists in continually sucking orderliness from its environment." (Erwin Schrödinger, "What is Life?", 1944)

"All nature is a continuum. The endless complexity of life is organized into patterns which repeat themselves - theme and variations - at each level of system. These similarities and differences are proper concerns for science. From the ceaseless streaming of protoplasm to the many-vectored activities of supranational systems, there are continuous flows through living systems as they maintain their highly organized steady states." (James G Miller, "Living Systems", 1978)

"All living organisms must feed on continual flows of matter and energy: from their environment to stay alive, and all living organisms continually produce waste. However, an ecosystem generates no net waste, one species' waste being another species' food. Thus, matter cycles continually through the web of life." (Fritjof Capra, "The Hidden Connections", 2002)

On Conjecture (Unsourced)

"In the study of Nature conjecture must be entirely put aside, and vague hypothesis carefully guarded against. The study of Nature begins with facts, ascends to laws, and raises itself, as far as the limits of man’s intellect will permit, to the knowledge of causes, by the threefold means of observation, experiment and logical deduction." (Jean Baptiste-Andre Dumas)

"Indeed, when in the course of a mathematical investigation we encounter a problem or conjecture a theorem, our minds will not rest until the problem is exhaustively solved and the theorem rigorously proved; or else, until we have found the reasons which made success impossible and, hence, failure unavoidable. Thus, the proofs of the impossibility of certain solutions plays a predominant role in modern mathematics; the search for an answer to such questions has often led to the discovery of newer and more fruitful fields of endeavour." (David Hilbert)

"The conjectures of the scientific intelligence are genuine creative novelties, inherently unpredictable and not determined by the character of the scientist’s physical environment. The thinking mind is not a causal mechanism." (Anthony M Quinton)

"The only use of an hypothesis is, that it should lead to experiments; that it should be a guide to facts. In this application, conjectures are always of use. The destruction of an error hardly ever takes place without the discovery of truth. [...] Hypothesis should be considered merely an intellectual instrument of discovery, which at any time may be relinquished for a better instrument. It should never be spoken of as truth; its highest praise is verisimility. Knowledge can only be acquired by the senses; nature has an archetype in the human imagination; her empire is given only to industry and action, guided and governed by experience." (Sir Humphry Davy) 

"The purpose of life is to conjecture and prove." (Paul Erdős)

"The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations." (Godfrey H Hardy)

"What certainty can there be in a Philosophy which consists in as many Hypotheses as there are Phaenomena to be explained. To explain all nature is too difficult a task for any one man or even for any one age. 'Tis much better to do a little with certainty, & leave the rest for others that come after you, than to explain all things by conjecture without making sure of any thing." (Sir Isaac Newton)

On Conjecture (1800-1899)

"In order to supply the defects of experience, we will have recourse to the probable conjectures of analogy, conclusions which we will bequeath to our posterity to be ascertained by new observations, which, if we augur rightly, will serve to establish our theory and to carry it gradually nearer to absolute certainty." (Johann H Lambert, "The System of the World", 1800)

"In all speculations on the origin, or agents that have produced the changes on this globe, it is probable that we ought to keep within the boundaries of the probable effects resulting from the regular operations of the great laws of nature which our experience and observation have brought within the sphere of our knowledge. When we overleap those limits, and suppose a total change in nature's laws, we embark on the sea of uncertainty, where one conjecture is perhaps as probable as another; for none of them can have any support, or derive any authority from the practical facts wherewith our experience has brought us acquainted." (William Maclure, "Observations on the Geology of the United States of America", 1817)

"The science of the mathematics performs more than it promises, but the science of metaphysics promises more than it performs. The study of the mathematics, like the Nile, begins in minuteness but ends in magnificence; but the study of metaphysics begins with a torrent of tropes, and a copious current of words, yet loses itself at last in obscurity and conjecture, like the Niger in his barren deserts of sand." (Charles C Colton, "Lacon", 1820)

"We know the effects of many things, but the causes of few; experience, therefore, is a surer guide than imagination, and inquiry than conjecture." (Charles C Colton, "Lacon", 1820)

"Let me be permitted to recall that the object of mathematics is not to investigate the causes that one can assign to natural phenomena. This science would lose both its character and credit if, renouncing the support of general well-confirmed facts, it sought within the realm of nebulous conjectures, a realm which has always been a fertile source of error for ways of satisfying the thirst fo rexplanation." (Sophie Germain, "Examen des principes qui peuvent conduire a la connaissance des lois de requilibre et du mouvement des solides elastiques", Annales de Chimie 38, 1828)

"Life is not the object of Science: we see a little, very little; And what is beyond we can only conjecture." (Samuel Johnson, "Causes Which Produce Diversity of Opinion", 1840)

"The entire annals of Observation probably do not elsewhere exhibit so extraordinary a verification of any theoretical conjecture adventured on by the human spirit!" (John P Nichol, "The Planet Neptune: An Exposition and History", 1848)

"The philosophical study of nature rises above the requirements of mere delineation, and does not consist in the sterile accumulation of isolated facts. The active and inquiring spirit of man may therefore be occasionally permitted to escape from the present into the domain of the past, to conjecture that which cannot yet be clearly determined, and thus to revel amid the ancient and ever-recurring myths of geology." (Alexander von Humboldt, "Views of Nature: Or Contemplation of the Sublime Phenomena of Creation", 1850)

"The rules of scientific investigation always require us, when we enter the domains of conjecture, to adopt that hypothesis by which the greatest number of known facts and phenomena may be reconciled." (Matthew F Maury, "The Physical Geography of the Sea", 1855)

"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact." (Samuel L Clemens [Mark Twain], "Life on the Mississippi", 1883)

"I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain. [...] But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors." (Hermann von Helmholtz, 1891)

On Randomness XXVI (Universe)

"Random chance was not a sufficient explanation of the Universe - in fact, random chance was not sufficient to explain random chance; the pot could not hold itself." (Robert A Heinlein, "Stranger in a Strange Land", 1961)

"The line between inner and outer landscapes is breaking down. Earthquakes can result from seismic upheavals within the human mind. The whole random universe of the industrial age is breaking down into cryptic fragments." (William S Burroughs, [preface] 1972)

"There is no reason to assume that the universe has the slightest interest in intelligence -  or even in life. Both may be random accidental by-products of its operations like the beautiful patterns on a butterfly's wings. The insect would fly just as well without them […]" (Arthur C Clarke, "The Lost Worlds of 2001", 1972)

"It is tempting to wonder if our present universe, large as it is and complex though it seems, might not be merely the result of a very slight random increase in order over a very small portion of an unbelievably colossal universe which is virtually entirely in heat-death." (Isaac Asimov, 1976)

"Perhaps randomness is not merely an adequate description for complex causes that we cannot specify. Perhaps the world really works this way, and many events are uncaused in any conventional sense of the word." (Stephen J Gould, "Hen's Teeth and Horse's Toes", 1983)

"The world of science lives fairly comfortably with paradox. We know that light is a wave and also that light is a particle. The discoveries made in the infinitely small world of particle physics indicate randomness and chance, and I do not find it any more difficult to live with the paradox of a universe of randomness and chance and a universe of pattern and purpose than I do with light as a wave and light as a particle. Living with contradiction is nothing new to the human being." (Madeline L'Engle, "Two-Part Invention: The Story of a Marriage", 1988)

"Intriguingly, the mathematics of randomness, chaos, and order also furnishes what may be a vital escape from absolute certainty - an opportunity to exercise free will in a deterministic universe. Indeed, in the interplay of order and disorder that makes life interesting, we appear perpetually poised in a state of enticingly precarious perplexity. The universe is neither so crazy that we can’t understand it at all nor so predictable that there’s nothing left for us to discover." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1997)

"Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"The first view of randomness is of clutter bred by complicated entanglements. Even though we know there are rules, the outcome is uncertain. Lotteries and card games are generally perceived to belong to this category. More troublesome is that nature's design itself is known imperfectly, and worse, the rules may be hidden from us, and therefore we cannot specify a cause or discern any pattern of order. When, for instance, an outcome takes place as the confluence of totally unrelated events, it may appear to be so surprising and bizarre that we say that it is due to blind chance." (Edward Beltrami. "What is Random?: Chance and Order in Mathematics and Life", 1999)

"The tissue of the world is built from necessities and randomness; the intellect of men places itself between both and can control them; it considers the necessity and the reason of its existence; it knows how randomness can be managed, controlled, and used." (Johann Wolfgang von Goethe)

On Coincidence IV (From Fiction to Science Fiction)

"He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind if it is applied to no larger system than the starry one." (Henry D Thoreau, "A Week on the Concord and Merrimack Rivers", 1849)

"There is in life an element of elfin coincidence which people reckoning on the prosaic may perpetually miss. As it has been well expressed in the paradox of Poe, wisdom should reason on the unforeseen." (Gilbert K Chesterton, "The Father Brown omnibus", 1951)

"In a world that operates largely at random, coincidences are to be expected, but any one of them must always be mistrusted." (Rex Stout, "Champagne for One", 1958)

"There is no coincidence. Only the illusion of coincidence." (Alan Moore, "V for Vendetta", 1982)

"Coincidence is the word we use when we can't see the levers and pulleys." (Emma Bull, "Bone Dance: A Fantasy for Technophiles", 1991)

"Coincidence is just the word we use when we have not yet discovered the cause." (Orson Scott Card, "The Call Of Earth", 1992)

"If you stare long enough at anything, you will start to find similarities. The word 'coincidence' exists in order to stop people from seeing meaning where none exists." (Chuck Klosterman, "Eating the Dinosaur", 2009)

"When there are strange things going on all around, every coincidence should be considered very carefully." (Sergei Lukyanenko, "The New Watch", 2013)

On Coincidence II

"People are entirely too disbelieving of coincidence. They are far too ready to dismiss it and to build arcane structures of extremely rickety substance in order to avoid it. I, on the other hand, see coincidence everywhere as an inevitable consequence of the laws of probability, according to which having no unusual coincidence is far more unusual than any coincidence could possibly be." (Isaac Asimov, "The Planet That Wasn't", 1976)

"Our form of life depends, in delicate and subtle ways, on several apparent ‘coincidences’ in the fundamental laws of nature which make the Universe tick. Without those coincidences, we would not be here to puzzle over the problem of their existence […] What does this mean? One possibility is that the Universe we know is a highly improbable accident, ‘just one of those things’." (John R Gribbin, "Genesis: The Origins of Man and the Universe", 1981)

"[…] a mathematician's ultimate concern is that his or her inventions be logical, not realistic. This is not to say, however, that mathematical inventions do not correspond to real things. They do, in most, and possibly all, cases. The coincidence between mathematical ideas and natural reality is so extensive and well documented, in fact, that it requires an explanation. Keep in mind that the coincidence is not the outcome of mathematicians trying to be realistic - quite to the contrary, their ideas are often very abstract and do not initially appear to have any correspondence to the real world. Typically, however, mathematical ideas are eventually successfully applied to describe real phenomena […]"(Michael Guillen, "Bridges to Infinity: The Human Side of Mathematics", 1983)

"Moreover, joint occurrences tend to be better recalled than instances when the effect does not occur. The proneness to remember confirming instances, but to overlook disconfirming ones, further serves to convert, in thought, coincidences into causalities." (Albert Bandura, "Social Foundations of Thought and Action: A social cognitive theory", 1986)

"There is no coherent knowledge, i.e. no uniform comprehensive account of the world and the events in it. There is no comprehensive truth that goes beyond an enumeration of details, but there are many pieces of information, obtained in different ways from different sources and collected for the benefit of the curious. The best way of presenting such knowledge is the list - and the oldest scientific works were indeed lists of facts, parts, coincidences, problems in several specialized domains." (Paul K Feyerabend, "Farewell to Reason", 1987)

"A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)

"The law of truly large numbers states: With a large enough sample, any outrageous thing is likely to happen." (Frederick Mosteller, "Methods for Studying Coincidences", Journal of the American Statistical Association Vol. 84, 1989)

"Most coincidences are simply chance events that turn out to be far more probable than many people imagine." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1997)

"Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"Randomness is the very stuff of life, looming large in our everyday experience. […] The fascination of randomness is that it is pervasive, providing the surprising coincidences, bizarre luck, and unexpected twists that color our perception of everyday events." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

On Generalization (1970-1979)

"Accordingly there are two main types of science, exact science [...] and empirical science [...] seeking laws which are generalizations from particular experiences and are verifiable (or, more strictly, 'probabilities') only by observation and experiment." (Errol E Harris, "Hypothesis and Perception: The Roots of Scientific Method", 1970)

"One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently, generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is ‘really there’." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1970)

"Science uses the senses but does not enjoy them; finally buries them under theory, abstraction, mathematical generalization." (Theodore Roszak, "Where the Wasteland Ends", 1972)

"A single observation that is inconsistent with some generalization points to the falsehood of the generalization, and thereby 'points to itself'." (Ian Hacking, "The Emergence Of Probability", 1975)

"The sciences have started to swell. Their philosophical basis has never been very strong. Starting as modest probing operations to unravel the works of God in the world, to follow its traces in nature, they were driven gradually to ever more gigantic generalizations. Since the pieces of the giant puzzle never seemed to fit together perfectly, subsets of smaller, more homogeneous puzzles had to be constructed, in each of which the fit was better." (Erwin Chargaff, "Voices in the Labyrinth", 1975)

"The word generalization in literature usually means covering too much territory too thinly to be persuasive, let alone convincing. In science, however, a generalization means a principle that has been found to hold true in every special case. [...] The principle of leverage is a scientific generalization." (Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)

"And when such claims are extraordinary, that is, revolutionary in their implications for established scientific generalizations already accumulated and verified, we must demand extraordinary proof." (Marcello Truzzi, Zetetic Scholar, Vol. 1 (1), 1976)

"If it is to be effective as a tool of thought, a notation must allow convenient expression not only of notions arising directly from a problem, but also of those arising in subsequent analysis, generalization, and specialization." (Kenneth E Iverson, "Notation as a Tool of Thought", 1979)

"Prediction can never be absolutely valid and therefore science can never prove some generalization or even test a single descriptive statement and in that way arrive at final truth." (Gregory Bateson, "Mind and Nature, A necessary unity", 1979)

On Technology III

"Technology means the systematic application of scientific or other organized knowledge to practical tasks." (John K Galbraith, "The New Industrial State", 1967)

"Networks constitute the new social morphology of our societies, and the diffusion of networking logic substantially modifies the operation and outcomes in processes of production, experience, power, and culture. While the networking form of social organization has existed in other times and spaces, the new information technology paradigm provides the material basis for its pervasive expansion throughout the entire social structure." (Manuel Castells, "The Rise of the Network Society", 1996)

"Beauty is more important in computing than anywhere else in technology because software is so complicated. Beauty is the ultimate defense against complexity." (David Gelernter, "Machine Beauty: Elegance And The Heart Of Technolog", 1998)

"Modelling techniques on powerful computers allow us to simulate the behaviour of complex systems without having to understand them.  We can do with technology what we cannot do with science.  […] The rise of powerful technology is not an unconditional blessing.  We have  to deal with what we do not understand, and that demands new  ways of thinking." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)

"A primary reason that evolution - of life-forms or technology - speeds up is that it builds on its own increasing order." (Ray Kurzweil, "The Age of Spiritual Machines: When Computers Exceed Human Intelligence", 1999) 

"As systems became more varied and more complex, we find that no single methodology suffices to deal with them. This is particularly true of what may be called information intelligent systems - systems which form the core of modern technology. To conceive, design, analyze and use such systems we frequently have to employ the totality of tools that are available. Among such tools are the techniques centered on fuzzy logic, neurocomputing, evolutionary computing, probabilistic computing and related methodologies. It is this conclusion that formed the genesis of the concept of soft computing." (Lotfi A Zadeh, "The Birth and Evolution of Fuzzy Logic: A personal perspective", 1999)

"We do not learn much from looking at a model - we learn more from building the model and manipulating it. Just as one needs to use or observe the use of a hammer in order to really understand its function, similarly, models have to be used before they will give up their secrets. In this sense, they have the quality of a technology - the power of the model only becomes apparent in the context of its use." (Margaret Morrison & Mary S Morgan, "Models as mediating instruments", 1999)

"Periods of rapid change and high exponential growth do not, typically, last long. A new equilibrium with a new dominant technology and/or competitor is likely to be established before long. Periods of punctuation are therefore exciting and exhibit unusual uncertainty. The payoff from establishing a dominant position in this short time is therefore extraordinarily high. Dominance is more likely to come from skill in marketing and positioning than from superior technology itself." (Richar Koch, "The Power Laws", 2000)

"Mythology and science both extend the scope of human beings. Like science and technology, mythology, as we shall see, is not about opting out of this world, but about enabling us to live more intensely within it." (Karen Armstrong, "A Short History Of Myth", 2004)

"In an age when technology is integrating us more tightly together and delivering tremendous flows of innovation, knowledge, connectivity and commerce, the future belongs to those who build webs not walls, who can integrate not separate, to get the most out of these flows." (Thomas L Friedman, The New York Times, 2016)

Machines XI (Life vs. Machine II)

"The moral universe is so closely linked to the physical universe that it is scarcely likely that they are not one and the same machine." (Denis Diderot, "Eléments de Physiologie", 1875)

"Thanks to the psycho-physical reversibility, we can materialize the act of creation. Undoubtedly, the inventive machine has not yet been created, but we can see its creation soon." (Stefan Odobleja, "Consonant Psychology", 1938)

"In any case there is an intense modern interest in machines that imitate life. The great difference between magic and the scientific imitation of life is that where the former is content to copy external appearance, the latter is concerned more with performance and behavior." (William G Walter," An imitation of life", 1950) 

"We are always looking for metaphors in which to express our ideas of life, for our language is inadequate for all its complexities. Life is a labyrinth.[...] Life is a machine.[...] Life is a laboratory.[...] It is but a metaphor. When we speak of ultimate things we can, maybe, speak only in metaphors. Life is a dance, a very elaborate and complex dance [...]." (Charles Singer, "A Short History of Scientific Ideas to 1900", 1959)

"The machine rules. Human life is rigorously controlled by it, dominated by the terribly precise will of mechanisms. These creatures of man are exacting. They are now reacting on their creators, making them like themselves. They want well-trained humans; they are gradually wiping out the differences between men, fitting them into their own orderly functioning, into the uniformity of their own regimes. They are thus shaping humanity for their own use, almost in their own image." (Paul A Valéry, "Fairy Tales for Computers", 1969)

"The environment makes up a huge, enormously complex living machine that forms a thin dynamic layer on the earth’s surface, and every human activity depends on the integrity and the proper functioning of this machine. Without the photosynthetic activity of green plants, there would be no oxygen for our engines, smelters, and furnaces, let alone support for human and animal life. Without the action of the plants, animals, and microorganisms that live in them, we could have no pure water in our lakes and rivers. Without the biological processes that have gone on in the soil for thousands of years, we could have neither food crops, oil, nor coal. This machine is our biological capital, the basic apparatus on which our total productivity depends. If we destroy it, our most advanced technology will become useless and any economic and political system that depends on it will founder. The environmental crisis is a signal of this approaching catastrophe." (Barry Commoner, "The Closing Circle: Nature, Man & Technology", 1971)

"In his emotional involvement with the machine, the engineer cannot help but feel at times that he has come face to face with a strange but potent form of life." (Samuel C Florman, "The Existential Pleasures of Engineering", 1976)

"Life, a watery, carbon-based macromolecular system, is reproducing autopoeisis. The autopoetic view of life is circular. Life is a metabolic machine which not only reproduces but fi ercely stores and uses information in order to resist breaking down." (Lynn Margulis & Dorion Sagan, "Microcosmos", 1986)

"On balance, the cartesian metaphor of organism as machine has proved to be a good idea. Ideas do not have to be correct in order to be good; its only necessary that, if they do fail, they do so in an interesting way." (Robert Rosen)

K W Friedrich von Schlegel - Collected Quotes

"It is in fact wonderful how physics - as soon as it is concerned not with technical purposes but with general results - without knowing it gets into cosmogony, astrology, theosophy, or whatever you wish to call it, in short, into a mystic discipline of the whole." (K W Friedrich von Schlegel, "Dialogue on Poetry and Literary Aphorisms", 1797)

"There are three kinds of explanation in science: explanations which throw a light upon, or give a hint at a matter; explanations which do not explain anything; and explanations which obscure everything." (K W Friedrich von Schlegel, "Dialogue on Poetry and Literary Aphorisms", 1797) 

"Wit is the appearance, the external flash of imagination. Thus its divinity, and the witty character of mysticism." (K W Friedrich von Schlegel, "Dialogue on Poetry and Literary Aphorisms", [Aphorism 26] 1797)

"Only he who possesses a personal religion, an original view of infinity, can be an artist." (K W Friedrich von Schlegel, "Selected Ideas", 1799-1800)

"Think of something finite molded into the infinite, and you think of man." (K W Friedrich von Schlegel, "Selected Ideas", 1799-1800)

"In the same way as philosophy loses sight of its true object and appropriate matter, when either it passes into and merges in theology, or meddles with external politics, so also does it mar its proper form when it attempts to mimic the rigorous method of mathematics." (K W Friedrich von Schlegel, "Philosophy of Life", 1828)

"The true excellence and importance of those arts and sciences which exert and display themselves in writing, may be seen, in a more general point of view, in the great influence which they have exerted on the character and fate of nations, throughout the history of the world." (K W Friedrich von Schlegel, "Lectures on the History of Literature, Ancient and Modern", 1841)

"The mind understands something only insofar as it absorbs it like a seed into itself, nurtures it, and lets it grow into blossom and fruit." (K W Friedrich von Schlegel, "Ideas, Lucinde and the Fragments", 1991)

"Whatever can be done while poetry and philosophy are separated has been done and accomplished. So the time has come to unite the two." (K W Friedrich von Schlegel, "Ideas, Lucinde and the Fragments", 1991)

"Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry." (Friedrich von Schlegel)

Thomas H Huxley - Collected Quotes

"Living things have no inertia, and tend to no equilibrium." (Thomas H Huxley, "On the Educational Value of the Natural History Sciences", 1854)

"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)

"Science has fulfilled her function when she has ascertained and enunciated truth."  (Thomas H Huxley, "Man's Place in Nature.", 1863)

"The method of scientific investigation is nothing but the expression of the necessary mode of working of the human mind. (Thomas H Huxley, "Our Knowledge of the Causes of the Phenomena of Organic Nature", 1863)

"Mathematical training is almost purely deductive. The mathematician starts with a few simple propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them." (Thomas H Huxley, "Scientific Education: Notes of an After Dinner Speech", Macmillan’s Magazine Vol. XX, 1869)

"The mathematician starts with a few propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them. The teaching of languages, at any rate as ordinarily practised, is of the same general nature: authority and tradition furnish the data, and the mental operations are deductive." (Thomas H Huxley, 1869)

"[...] there can be little doubt that the further science advances, the more extensively and consistently will all the phenomena of Nature be represented by materialistic formulae and symbols." (Thomas H Huxley, "On the Physical Basis of Life", 1869)

"[Mathematics] is that [subject] which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870)

"The great tragedy of Science - the slaying of a beautiful hypothesis by an ugly fact." (Thomas H Huxley, "Biogenesis and abiogenesis", [address] 1870)

"The Mathematician deals with two properties of objects only, number and extension, and all the inductions he wants have been formed and finished ages ago. He is now occupied with nothing but deductions and verification." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870)

"Therefore, the great business of the scientific teacher is, to imprint the fundamental, irrefragable facts of his science, not only by words upon the mind, but by sensible impressions upon the eye, and ear, and touch of the student, in so complete a manner, that every term used, or law enunciated, should afterwards call up vivid images of the particular structural, or other, facts which furnished the demonstration of the law, or the illustration of the term." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870) 

"You may read any quantity of books, and you may be almost as ignorant as you were at starting, if you don’t have, at the back of your minds, the change for words in definite images which can only be acquired through the operation of your observing faculties on the phenomena of nature." (Thomas H Huxley, "Science and Education", 1877)

"It sounds paradoxical to say the attainment of scientific truth has been effected, to a great extent, by the help of scientific errors." (Thomas H Huxley, "The Progress of Science", 1887)

"All artificial education ought to be an anticipation of natural education."  (Thomas H Huxley, "Science and Education", 1891)

"All truth, in the long run, is only common sense clarified." (Thomas H Huxley, "Science and Education", 1891)

"Education is the instruction of the intellect in the laws of Nature, under which name I include not merely things and their forces, but men and their ways; and the fashioning of the affections and of the will into an earnest and loving desire to move in harmony with those laws." (Thomas H Huxley, "Science and Education", 1891)

"It is not a question whether one order of study or another should predominate. It is a question of what topics of education you shall elect which will combine all the needful elements in such due proportion as to give the greatest amount of food, support, and encouragement to those faculties which enable us to appreciate truth, and to profit by those sources of innocent happiness which are open to us, and, at the same time, to avoid that which is bad, and coarse, and ugly, and keep clear of the multitude of pitfalls and dangers which beset those who break through the natural or moral laws." (Thomas H Huxley, "Science and Education", 1891)

"Many of the faults and mistakes of the ancient philosophers are traceable to the fact that they knew no language but their own, and were often led into confusing the symbol with the thought which it embodied." (Thomas H Huxley, "Science and Education", 1891)

"There is but one right, and the possibilities of wrong are infinite." (Thomas H Huxley, "Science and Education", 1891)

"Accuracy is the foundation of everything else." (Thomas H Huxley, "Method and Results", 1893)

"Anyone who is practically acquainted with scientific work is aware that those who refuse to go beyond fact, rarely get as far as fact; and anyone who has studied the history of science knows that almost every great step therein has been made by the 'anticipation of Nature.'" (Thomas H Huxley, "Method and Results", 1893)

"The 'Law of Nature' is not a command to do, or to refrain from doing, anything. It contains, in reality, nothing but a statement of that which a given being tends to do under the circumstances of its existence; and which, in the case of a living and sensitive being, it is necessitated to do, if it is to escape certain kinds of disability, pain, and ultimate dissolution." (Thomas H Huxley, "Method and Results", 1893)

"The man of science has learned to believe in justification, not by faith, but by verification." (Thomas H Huxley, "Method and Results", 1893)

"The man of science, who, forgetting the limits of philosophical inquiry, slides from these formulæ and symbols into what is commonly understood by materialism, seems to me to place himself on a level with the mathematician, who should mistake the x's and y's with which he works his problems for real entities - and with this further disadvantage, as compared with the mathematician, that the blunders of the latter are of no practical consequence, while the errors of systematic materialism may paralyse the energies and destroy the beauty of a life." (Thomas H Huxley, "Method and Results", 1893)

"The scientific imagination always restrains itself within the limits of probability." (Thomas H Huxley, "Science and Christian Tradition", 1893)

"Thought is existence. More than that, so far as we are concerned, existence is thought, all our conceptions of existence being some kind or other of thought." (Thomas H Huxley, "Method and Results", 1893)

"Harmonious order governing eternally continuous progress - the web and woof of matter and force interweaving by slow degrees, without a broken thread, that veil which lies between us and the Infinite - that universe which alone we know or can know; such is the picture which science draws of the world, and in proportion as any part of that picture is in unison with the rest, so may we feel sure that it is rightly painted." (Thomas H Huxley, "Darwiniana", 1893–94)

"The method of scientific investigation is nothing but the expression of the necessary mode of working of the human mind. It is simply the mode in which all phenomena are reasoned about, rendered precise and exact." (Thomas H Huxley, "Method and Results", 1893)

"The scientific spirit is of more value than its products, and irrationally held truths may be more harmful than reasoned errors." (Thomas H Huxley, "Darwiniana", 1893–94)

"Whatever happens, science may bide her time in patience and in confidence." (Thomas H Huxley, "Science and Christian Tradition", 1893)

"Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulæ will not get a definite result out of loose data." (Thomas H Huxley, "Discourses, Biological and Geological", 1894)

"In the world of letters, learning and knowledge are one, and books are the source of both; whereas in science, as in life, learning and knowledge are distinct, and the study of things, and not of books, is the source of the latter." (Thomas H Huxley, "Discourses, Biological and Geological", 1894)

"Perhaps the most valuable result of all education is the ability to make yourself do the thing you have to do, when it ought to be done, whether you like it or not; it is the first lesson that ought to be learned; and however early a man's training begins, it is probably the last lesson that he learns thoroughly." (Thomas H Huxley)

George Santayana - Collected Quotes

"Symmetry is evidently a kind of unity in variety, where a whole is determined by the rhythmic repetition of similar." (George Santayana, "The Sense of Beauty: Being the Outlines of Aesthetic Theory", 1896)

"The scientific value of truth is not, however, ultimate or absolute. It rests partly on practical, partly on aesthetic interests. As our ideas are gradually brought into conformity with the facts by the painful process of selection, - for intuition runs equally into truth and into error, and can settle nothing if not controlled by experience, - we gain vastly in our command over our environment. This is the fundamental value of natural science." (George Santayana, "The Sense of Beauty: Being the Outlines of Aesthetic Theory", 1896)

"No system would have ever been framed if people had been simply interested in knowing what is true, whatever it may be. What produces systems is the interest in maintaining against all comers that some favourite or inherited idea of ours is sufficient and right. A system may contain an account of many things which, in detail, are true enough; but as a system, covering infinite possibilities that neither our experience nor our logic can prejudge, it must be a work of imagination and a piece of human soliloquy: It may be expressive of human experience, it may be poetical; but how should anyone who really coveted truth suppose that it was true?" (George Santayana, "The Genteel Tradition in American Philosophy", 1911)

"If all the arts aspire to the condition of music, all the sciences aspire to the condition of mathematics." (George Santayana, Some Turns of Thought in Modern Philosophy: Five Essays, 1933)

"[…] mathematics is like music, freely exploring the possibilities of form. And yet, notoriously, mathematics holds true of things; hugs and permeates them far more closely than does confused and inconstant human perception; so that the dream of many exasperated critics of human error has been to assimilate all science to mathematics, so as to make knowledge safe by making it, as Locke wished, direct perception of the relations between ideas […]" (George Santayana, "The Realm of Truth: Book Third of Realms of Being", 1937)

"Science, then, is the attentive consideration of common experience; it is common knowledge extended and refined. Its validity is of the same order as that of ordinary perception; memory, and understanding. Its test is found, like theirs, in actual intuition, which sometimes consists in perception and sometimes in intent." (George Santayana, "The Life of Reason, or the Phases of Human Progress", 1954)

 "Theory helps us to bear our ignorance of facts." (George Santayana)

On Randomness XII (Chaos I)

"Chaos is but unperceived order; it is a word indicating the limitations of the human mind and the paucity of observational facts. The words ‘chaos’, ‘accidental’, ‘chance’, ‘unpredictable’ are conveniences behind which we hide our ignorance." (Harlow Shapley, "Of Stars and Men: Human Response to an Expanding Universe", 1958)

"The term ‘chaos’ currently has a variety of accepted meanings, but here we shall use it to mean deterministically, or nearly deterministically, governed behavior that nevertheless looks rather random. Upon closer inspection, chaotic behavior will generally appear more systematic, but not so much so that it will repeat itself at regular intervals, as do, for example, the oceanic tides." (Edward N Lorenz, "Chaos, spontaneous climatic variations and detection of the greenhouse effect", 1991)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"In nonlinear systems - and the economy is most certainly nonlinear - chaos theory tells you that the slightest uncertainty in your knowledge of the initial conditions will often grow inexorably. After a while, your predictions are nonsense." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"Intriguingly, the mathematics of randomness, chaos, and order also furnishes what may be a vital escape from absolute certainty - an opportunity to exercise free will in a deterministic universe. Indeed, in the interplay of order and disorder that makes life interesting, we appear perpetually poised in a state of enticingly precarious perplexity. The universe is neither so crazy that we can’t understand it at all nor so predictable that there’s nothing left for us to discover." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1997)

"When we look at the world around us, we find that we are not thrown into chaos and randomness but are part of a great order, a grand symphony of life. Every molecule in our body was once a part of previous bodies-living or nonliving-and will be a part of future bodies. In this sense, our body will not die but will live on, again and again, because life lives on. We share not only life's molecules but also its basic principles of organization with the rest of the living world. Arid since our mind, too, is embodied, our concepts and metaphors are embedded in the web of life together with our bodies and brains. We belong to the universe, we are at home in it, and this experience of belonging can make our lives profoundly meaningful." (Fritjof Capra, "The Hidden Connections", 2002)

"[…] we would like to observe that the butterfly effect lies at the root of many events which we call random. The final result of throwing a dice depends on the position of the hand throwing it, on the air resistance, on the base that the die falls on, and on many other factors. The result appears random because we are not able to take into account all of these factors with sufficient accuracy. Even the tiniest bump on the table and the most imperceptible move of the wrist affect the position in which the die finally lands. It would be reasonable to assume that chaos lies at the root of all random phenomena." (Iwo Białynicki-Birula & Iwona Białynicka-Birula, "Modeling Reality: How Computers Mirror Life", 2004) 

"Although the potential for chaos resides in every system, chaos, when it emerges, frequently stays within the bounds of its attractor(s): No point or pattern of points is ever repeated, but some form of patterning emerges, rather than randomness. Life scientists in different areas have noticed that life seems able to balance order and chaos at a place of balance known as the edge of chaos. Observations from both nature and artificial life suggest that the edge of chaos favors evolutionary adaptation." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)

"Most systems in nature are inherently nonlinear and can only be described by nonlinear equations, which are difficult to solve in a closed form. Non-linear systems give rise to interesting phenomena such as chaos, complexity, emergence and self-organization. One of the characteristics of non-linear systems is that a small change in the initial conditions can give rise to complex and significant changes throughout the system." (Robert K Logan, "The Poetry of Physics and The Physics of Poetry", 2010)

"A system in which a few things interacting produce tremendously divergent behavior; deterministic chaos; it looks random but its not." (Christopher Langton) 

On Randomness X (From Fiction to Science-Fiction)

"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)

"The line between inner and outer landscapes is breaking down. Earthquakes can result from seismic upheavals within the human mind. The whole random universe of the industrial age is breaking down into cryptic fragments." (William S Burroughs, [preface] 1972)

"There is no reason to assume that the universe has the slightest interest in intelligence -  or even in life. Both may be random accidental by-products of its operations like the beautiful patterns on a butterfly's wings. The insect would fly just as well without them […]" (Arthur C Clarke, "The Lost Worlds of 2001", 1972)

"It is tempting to wonder if our present universe, large as it is and complex though it seems, might not be merely the result of a very slight random increase in order over a very small portion of an unbelievably colossal universe which is virtually entirely in heat-death." (Isaac Asimov, 1976)

"In the end, each life is no more than the sum of contingent facts, a chronicle of chance intersections, of flukes, of random events that divulge nothing but their own lack of purpose."

(Paul Auster, "The Locked Room", 1988)

"The natural world is full of irregularity and random alteration, but in the antiseptic, dust-free, shadowless, brightly lit, abstract realm of the mathematicians they like their cabbages spherical, please". (William A M Boyd, Brazzaville Beach, 1990)

"There are only patterns, patterns on top of patterns, patterns that affect other patterns. Patterns hidden by patterns. Patterns within patterns. If you watch close, history does nothing but repeat itself. What we call chaos is just patterns we haven't recognized. What we call random is just patterns we can't decipher. what we can't understand we call nonsense. What we can't read we call gibberish. There is no free will. There are no variables." (Chuck Palahniuk, "Survivor", 1999)

"Because the question for me was always whether that shape we see in our lives was there from the beginning or whether these random events are only called a pattern after the fact. Because otherwise we are nothing." (Cormac McCarthy, "All the Pretty Horses", 2010)

"All the ideas in the universe can be described by words. Therefore, if you simply take all the words and rearrange them randomly enough times, you’re bound to hit upon at least a few great ideas eventually."  (Jarod Kintz, "The Days of Yay are Here! Wake Me Up When They're Over", 2011)

"Chaos is impatient. It's random. And above all it's selfish. It tears down everything just for the sake of change, feeding on itself in constant hunger. But Chaos can also be appealing. It tempts you to believe that nothing matters except what you want." (Rick Riordan, "The Throne of Fire", 2011)

On Noise I

"Noise is the most impertinent of all forms of interruption. It is not only an interruption, but also a disruption of thought." (Arthur Schopenhauer, "Parerga and Paralipomena", 1851)

"Mathematics is the predominant science of our time; its conquests grow daily, though without noise; he who does not employ it for himself, will some day find it employed against himself." (Johann F Herbart, Werke, 1890)

"Life pushes its way through this fatalistically determined world like a river flowing upstream. It is a system of utterly improbable order, a message in a world of noise." (Joseph H Rush, "The Dawn of Life", 1957)

"Higher, directed forms of energy (e.g., mechanical, electric, chemical) are dissipated, that is, progressively converted into the lowest form of energy, i.e., undirected heat movement of molecules; chemical systems tend toward equilibria with maximum entropy; machines wear out owing to friction; in communication channels, information can only be lost by conversion of messages into noise but not vice versa, and so forth." (Ludwig von Bertalanffy, "Robots, Men and Minds", 1967)

"To adapt to a changing environment, the system needs a variety of stable states that is large enough to react to all perturbations but not so large as to make its evolution uncontrollably chaotic. The most adequate states are selected according to their fitness, either directly by the environment, or by subsystems that have adapted to the environment at an earlier stage. Formally, the basic mechanism underlying self-organization is the (often noise-driven) variation which explores different regions in the system’s state space until it enters an attractor. This precludes further variation outside the attractor, and thus restricts the freedom of the system’s components to behave independently. This is equivalent to the increase of coherence, or decrease of statistical entropy, that defines self-organization." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of 'nois' is officially admitted. The newer aspects of many fields start with the admission of uncertainty." (Richard Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"An essential element of dynamics systems is a positive feedback that self-enhances the initial deviation from the mean. The avalanche is proverbial. Cities grow since they attract more people, and in the universe, a local accumulation of dust may attract more dust, eventually leading to the birth of a star. Earlier or later, self-enhancing processes evoke an antagonistic reaction. A collapsing stock market stimulates the purchase of shares at a low price, thereby stabilizing the market. The increasing noise, dirt, crime and traffic jams may discourage people from moving into a big city." (Hans Meinhardt, "The Algorithmic Beauty of Sea Shells", 1995)

"Rather mathematicians like to look for patterns, and the primes probably offer the ultimate challenge. When you look at a list of them stretching off to infinity, they look chaotic, like weeds growing through an expanse of grass representing all numbers. For centuries mathematicians have striven to find rhyme and reason amongst this jumble. Is there any music that we can hear in this random noise? Is there a fast way to spot that a particular number is prime? Once you have one prime, how much further must you count before you find the next one on the list? These are the sort of questions that have tantalized generations." (Marcus du Sautoy, "The Music of the Primes", 1998)

"Data are collected as a basis for action. Yet before anyone can use data as a basis for action the data have to be interpreted. The proper interpretation of data will require that the data be presented in context, and that the analysis technique used will filter out the noise."  (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Data are generally collected as a basis for action. However, unless potential signals are separated from probable noise, the actions taken may be totally inconsistent with the data. Thus, the proper use of data requires that you have simple and effective methods of analysis which will properly separate potential signals from probable noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

On Randomness V (Systems I)

"Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Or are the contributing factors unknowable, and therefore render as random an outcome that can never be determined? Are seemingly random events merely the result of fluctuations superimposed on a determinate system, masking its predictability, or is there some disorderliness built into the system itself?” (Deborah J Bennett, "Randomness", 1998)

"The self-similarity of fractal structures implies that there is some redundancy because of the repetition of details at all scales. Even though some of these structures may appear to teeter on the edge of randomness, they actually represent complex systems at the interface of order and disorder."  (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"Emergent self-organization in multi-agent systems appears to contradict the second law of thermodynamics. This paradox has been explained in terms of a coupling between the macro level that hosts self-organization (and an apparent reduction in entropy), and the micro level (where random processes greatly increase entropy). Metaphorically, the micro level serves as an entropy 'sink', permitting overall system entropy to increase while sequestering this increase from the interactions where self-organization is desired." (H Van Dyke Parunak & Sven Brueckner, "Entropy and Self-Organization in Multi-Agent Systems", Proceedings of the International Conference on Autonomous Agents, 2001)

"Entropy [...] is the amount of disorder or randomness present in any system. All non-living systems tend toward disorder; left alone they will eventually lose all motion and degenerate into an inert mass. When this permanent stage is reached and no events occur, maximum entropy is attained. A living system can, for a finite time, avert this unalterable process by importing energy from its environment. It is then said to create negentropy, something which is characteristic of all kinds of life." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"If a network is solely composed of neighborhood connections, information must traverse a large number of connections to get from place to place. In a small-world network, however, information can be transmitted between any two nodes using, typically, only a small number of connections. In fact, just a small percentage of random, long-distance connections is required to induce such connectivity. This type of network behavior allows the generation of 'six degrees of separation' type results, whereby any agent can connect to any other agent in the system via a path consisting of only a few intermediate nodes." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)

"Although the potential for chaos resides in every system, chaos, when it emerges, frequently stays within the bounds of its attractor(s): No point or pattern of points is ever repeated, but some form of patterning emerges, rather than randomness. Life scientists in different areas have noticed that life seems able to balance order and chaos at a place of balance known as the edge of chaos. Observations from both nature and artificial life suggest that the edge of chaos favors evolutionary adaptation." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)

"Most systems in nature are inherently nonlinear and can only be described by nonlinear equations, which are difficult to solve in a closed form. Non-linear systems give rise to interesting phenomena such as chaos, complexity, emergence and self-organization. One of the characteristics of non-linear systems is that a small change in the initial conditions can give rise to complex and significant changes throughout the system. This property of a non-linear system such as the weather is known as the butterfly effect where it is purported that a butterfly flapping its wings in Japan can give rise to a tornado in Kansas. This unpredictable behaviour of nonlinear dynamical systems, i.e. its extreme sensitivity to initial conditions, seems to be random and is therefore referred to as chaos. This chaotic and seemingly random behaviour occurs for non-linear deterministic system in which effects can be linked to causes but cannot be predicted ahead of time." (Robert K Logan, "The Poetry of Physics and The Physics of Poetry", 2010)

"Second Law of thermodynamics is not an equality, but an inequality, asserting merely that a certain quantity referred to as the entropy of an isolated system - which is a measure of the system’s disorder, or ‘randomness’ - is greater (or at least not smaller) at later times than it was at earlier times." (Roger Penrose, "Cycles of Time: An Extraordinary New View of the Universe", 2010)

"[...] a high degree of unpredictability is associated with erratic trajectories. This not only because they look random but mostly because infinitesimally small uncertainties on the initial state of the system grow very quickly - actually exponentially fast. In real world, this error amplification translates into our inability to predict the system behavior from the unavoidable imperfect knowledge of its initial state." (Massimo Cencini, "Chaos: From Simple Models to Complex Systems", 2010)

"Although cascading failures may appear random and unpredictable, they follow reproducible laws that can be quantified and even predicted using the tools of network science. First, to avoid damaging cascades, we must understand the structure of the network on which the cascade propagates. Second, we must be able to model the dynamical processes taking place on these networks, like the flow of electricity. Finally, we need to uncover how the interplay between the network structure and dynamics affects the robustness of the whole system." (Albert-László Barabási, "Network Science", 2016)

On Entropy (From Fiction to Science-Fiction)

"One thinks one’s something unique and wonderful at the center of the universe. But in fact one’s merely a slight delay in the ongoing march of entropy." (Aldous Huxley, "Island", 1962)

"No structure, even an artificial one, enjoys the process of entropy. It is the ultimate fate of everything, and everything resists it." (Philip K Dick, "Galactic Pot-Healer", 1969)

"When things don't change any longer, that's the end result of entropy, the heat-death of the universe. The more things go on moving, interrelating, conflicting, changing, the less balance there is - and the more life." (Ursula K Le Guin, "The Lathe of Heaven", 1971)

"In the wastes of nonbeing it is born, flickers out, is born again and holds together, swells and spreads. In lifelessness it lives, against the gray tide of entropy it strives, improbably persists, gathering itself into ever richer complexities until it grows as a swelling wave. (James Tiptree Jr., "SheWaits for All Men Born", 1976)

"Her dance spoke of nothing more and nothing less than the tragedy of being alive, and being human. It spoke, most eloquently, of pain. It spoke, most knowingly, of despair. It spoke of the cruel humor of limitless ambition yoked to limited ability, of eternal hope invested in an ephemeral lifetime, of the driving need to try and create an inexorably predetermined future. It spoke of fear, and of hunger, and, most clearly, of the basic loneliness and alienation of the human animal. It described the universe through the eyes of man: a hostile environment, the embodiment of entropy, into which we are all thrown alone, forbidden by our nature to touch another mind save secondhand, by proxy. It spoke of the blind perversity which forces man to strive hugely for a peace which, once attained, becomes boredom. And it spoke of folly, of the terrible paradox by which man is simultaneously capable of reason and unreason, forever unable to cooperate even with himself." Spider Robinson and Jeanne Robinson, "Stardance", 1977)

"We see the universe as it is, Father Damien, and these naked truths are cruel ones. We who believe in life, and treasure it, will die. Afterward there will be nothing, eternal emptiness, blackness, nonexistence. In our living there has been no purpose, no poetry, no meaning. Nor do our deaths possess these qualities. When we are gone, the universe will not long remember us, and shortly it will be as if we had never lived at all. Our worlds and our universe will not long outlive us. Ultimately entropy will consume all, and our puny efforts cannot stay that awful end." (George R R Martin, "The Way of Cross and Dragon", 1979)

"But no longer were they always obedient to the mandates of their creators; like all material things, they were not immune to the corruptions of Time and its patient, unsleeping servant, Entropy." (Arthur C Clark, "3001: The Final Odyssey", 1997)

"Out of twinkling stardust all came, into dark matter all will fall. Death mocks us as we laugh defiance at entropy, yet ignorance birthed mortals sail forth upon time’s cruel sea." (Peter F Hamilton, "The Temporal Void", 2008)

"Yet, in the end, entropy will always emerge victorious, snuffing out the very last glimmer of heat and light. After that there is only darkness. When that state is reached even eternity will cease to exist, for one moment will be like every other and nothingness will claim the universe." (Peter F Hamilton, "The Temporal Void", 2008)

"Nothing up there tonight but entropy, and the same imaginary shapes that people had been imposing on nature since they’d first thought to wonder at the heavens." (Peter Watts, "Echopraxia", 2014)

"The process of thinking itself requires us to view the universe in the direction of entropy, since an abstraction always involves information loss, since symbols 'abstract' complexity from observed objects." (John C Wright, "Awake in the Night Land", 2014)

"And don’t ever make the mistake of thinking that things you didn’t intend or plan don’t matter. It’s a big, disorganised multiverse out there - an accident of stars. Almost nothing ever works out like we want it to, and when it does, there’s guaranteed to be unexpected consequences. Randomness is what separates life from entropy, but it’s also what makes it fun." (Foz Meadows, "An Accident of Stars", 2016)

"Entropy is just a fancy way of saying: things fall apart." (Dan Brown, "Origin", 2017)

James G Miller - Collected Quotes

"General systems theory is a series of related definitions, assumptions, and postulates about all levels of systems from atomic particles through atoms, molecules, crystals, viruses, cells, organs, individuals, small groups, societies, planets, solar systems, and galaxies. General behavior systems theory is a subcategory of such theory, dealing with living systems, extending roughly from viruses through societies. A significant fact about living things is that they are open systems, with important inputs and outputs. Laws which apply to them differ from those applying to relatively closed systems." (James G Miller, "General behavior systems theory and summary", Journal of Counseling Psychology 3 (2), 1956)

"In the most general mathematical sense, a space is a set of elements which conform to certain postulates." (James G Miller, "Living Systems: Basic Concepts", 1969) 

"My analysis of living systems uses concepts of thermodynamics, information theory, cybernetics, and systems engineering, as well as the classical concepts appropriate to each level. The purpose is to produce a description of living structure and process in terms of input and output, flows through systems, steady states, and feedbacks, which will clarify and unify the facts of life." (James G Miller, "Living Systems: Basic Concepts", 1969)

"All nature is a continuum. The endless complexity of life is organized into patterns which repeat themselves - theme and variations - at each level of system. These similarities and differences are proper concerns for science. From the ceaseless streaming of protoplasm to the many-vectored activities of supranational systems, there are continuous flows through living systems as they maintain their highly organized steady states." (James G Miller, "Living Systems", 1978)

"Living systems maintain a steady state of negative entropy even though entropic changes occur in them as they do everywhere else. This they do by taking in inputs of foods or fuels, matter-energy higher in complexity or organization or negentropy, i.e. lower in entropy, than their outputs." (James G Miller, "Living Systems", 1978)

"Most concrete systems have boundaries which are at least partially permeable, permitting sizable magnitudes of at least certain sorts of matter-energy or information transmissions to cross them […] such a system is an open system. A closed system, in contrast, is one with impermeable boundaries through which no matter-energy or information transmissions of any sort can occur. In open systems entropy may increase, remain in steady state, or decrease." (James G Miller,"Living Systems", 1978)

"My presentation of a general theory of living systems will employ two sorts of spaces in which they may exist, physical or geographical space and conceptual or abstract space [...] The characteristics and constraints of physical space affect the action of all concrete systems, living and nonliving [...] Physical space is a common space because it is the only space in which all concrete systems, living and nonliving, exist (though some may exist in other spaces simultaneously). Physical space is shared by all scientific observers, and all scientific data must be collected in it. This is equally true for natural science and behavioral science." (James G Miller, "Living Systems", 1978)

"The most general form of systems theory is a set of logical or mathematical statements about all conceptual systems. A subset of this concerns all concrete systems. A subsubset concerns the very special and very important living systems, i. e., general living systems theory." (James G Miller, "Living systems", 1978) 

"The structure of a system is the arrangement of its subsystems and components in three-dimensional space at a given moment of time. This always changes over time. It may remain relatively fixed for a long period or it may change from moment to moment, depending upon the characteristics of the process in the system. This process halted at any given moment, as when motion is frozen by a high-speed photograph, reveals the three-dimensional spatial arrangement of the system's components as of that instant." (James G Miller, "Living systems", 1978) 

"The term system has a number of meanings. There are systems of numbers and of equations, systems of value and of thought, systems of law, solar systems, organic systems, management systems, command and control systems, electronic systems, even the Union Pacific Railroad system. The meanings of 'system' are often confused. The most general, however, is: A system is a set of interacting units with relationships among them. The word 'set' implies that the units have some common properties. These common properties are essential if the units are to interact or have relationships. The state of each unit is constrained by, conditioned by, or dependent on the state of other units. The units are coupled. Moreover, there is at least one measure of the sum of its units which is larger than the sum of that measure of its units." (James G Miller, "Living systems", 1978) 

"It [Living Systems Theory (LST)] involves observing and measuring important relationships between inputs and outputs of the total system and identifying the structures that perform each of the sub‐system processes. […] The flows of relevant matter, energy, and information through the system and the adjustment processes of subsystems and the total system are also examined. The status and function of the system are analyzed and compared with what is average or normal for that type of system. If the system is experiencing a disturbance in some steady state, an effort is made to discover the source of the strain and correct it." (James G Miller & Jessie L Miller, "Applications of living systems theory", Systemic Practice and Action Research 8, 1995)

"The universe of all things that exist may be understood as a universe of systems where a system is defined as any set of related and interacting elements. This concept is primitive and powerful and has been used increasingly over the last half-century to organize knowledge in virtually all domains of interest to investigators. As human inventions and social interactions grow more complex, general conceptual frameworks that integrate knowledge among different disciplines studying those emerging systems grow more important. Living systems theory (LST) instructs integrative research among biological and social sciences and related academic disciplines." (G A Swanson & James G Miller, "Living Systems Theory", 2013)