On Paradoxes (2000-2009)

"One distinguishing feature of contemporary culture in America is that information is consumed for diversion rather than for consequential purposes. Paradoxically, in other words, information of all kinds is processed as low-level cognitive distraction, a form of mass entertainment. The collapsing of news, data, broadcast, and leisure media has resulted in an entertainment culture where the act of consuming information is as diversionary as watching a variety show or a situation comedy. [...] The simple term 'information' may no longer be adequate to describe the spectrum of input available to human beings in their capacities as data processors." (Joseph Urgo, "In the Age of Distraction", 2000)

"That is the paradox of the epidemic: that in order to create one contagious movement, you often have to create many small movements first." (Malcolm T Gladwell, "The Tipping Point: How Little Things Can Make a Big Difference", 2000)

"The motion of the mind is conveyed along a cloud of meaning. There is this paradox that we get to meaning only when we strip the meaning from symbols." (David Berlinski, "The Advent of the Algorithm: The Idea that Rules the World", 2000)

"Zero is powerful because it is infinity’s twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling. The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity. The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics, and of religion. Underneath every revolution lay a zero - and an infinity." (Charles Seife, "Zero: The Biography of a Dangerous Idea", 2000)

"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)

"The best reaction to a paradox is to invent a genuinely new and deep idea." (Ian Hacking, "An Introduction to Probability and Inductive Logic", 2001)

"As the least conscious layer of the user experience, the conceptual model has the paradoxical quality of also having the most impact on usability. If an appropriate conceptual model is faithfully represented throughout the interface, after users recognize and internalize the model, they will have a fundamental understanding of what the application does and how to operate it." (Bob Baxley, "Making the Web Work: Designing Effective Web Applications", 2002)

"A sudden change in the evolutive dynamics of a system (a ‘surprise’) can emerge, apparently violating a symmetrical law that was formulated by making a reduction on some (or many) finite sequences of numerical data. This is the crucial point. As we have said on a number of occasions, complexity emerges as a breakdown of symmetry (a system that, by evolving with continuity, suddenly passes from one attractor to another) in laws which, expressed in mathematical form, are symmetrical. Nonetheless, this breakdown happens. It is the surprise, the paradox, a sort of butterfly effect that can highlight small differences between numbers that are very close to one another in the continuum of real numbers; differences that may evade the experimental interpretation of data, but that may increasingly amplify in the system’s dynamics." (Cristoforo S Bertuglia & Franco Vaio, "Nonlinearity, Chaos, and Complexity: The Dynamics of Natural and Social Systems", 2003)

"Paradox is the sharpest scalpel in the satchel of science. Nothing concentrates the mind as effectively, regardless of whether it pits two competing theories against each other, or theory against observation, or a compelling mathematical deduction against ordinary common sense." (Hans Christian von Baeyer, "Information, The New Language of Science", 2003)

"An apparent paradox is that chaos is deterministic, generated by fixed rules which do not themselves involve any elements of change. We even speak of deterministic chaos. In principle, the future is completely determined by the past; but in practice small uncertainties, much like minute errors of measurement which enter into calculations, are amplified, with the effect that even though the behavior is predictable in the short term, it is unpredictable over the long term." (Heinz-Otto Peitgen et al, "Chaos and Fractals: New Frontiers of Science" 2nd Ed., 2004)

"Chaos theory, for example, uses the metaphor of the ‘butterfly effect’. At critical times in the formation of Earth’s weather, even the fluttering of the wings of a butterfly sends ripples that can tip the balance of forces and set off a powerful storm. Even the smallest inanimate objects sent back into the past will inevitably change the past in unpredictable ways, resulting in a time paradox." (Michio Kaku, "Parallel Worlds: A journey through creation, higher dimensions, and the future of the cosmos", 2004)

"Nature does weird things. It lives on the edge. But it is careful to bob and weave from the fatal punch of logical paradox." (Brian Greene, "The Fabric of the Cosmos: Space, Time, and the Texture of Reality", 2004)

"Although fiction is not fact, paradoxically we need some fictions, particularly mathematical ideas and highly idealized models, to describe, explain, and predict facts.  This is not because the universe is mathematical, but because our brains invent or use refined and law-abiding fictions, not only for intellectual pleasure but also to construct conceptual models of reality." (Mario Bunge, "Chasing Reality: Strife over Realism", 2006)

"One of the apparent paradoxes in probability is that, while the outcome of the next roll of a die or toss of a coin may be unpredictable, there are nevertheless underlying patterns in the outcomes overall. Specifically, when a fair die is rolled many times, there is a 'settling down' effect as the proportion of each outcome (1, 2, 3, …, 6) gradually approaches 1/6. In the limiting case, as the number of rolls reaches infinity, the shape of the probability distribution becomes uniform." (Alan Graham, "Developing Thinking in Statistics", 2006)

"The existing general descriptions of quantum theory emphasize puzzles and paradoxes in a way that tend to make non-physicists leery of using in any significant away the profound changes in our understanding of both man and nature wrought by the quantum revolution. Yet in the final analysis quantum mechanics is more understandable than classical mechanics because it is more deeply in line with our common sense ideas about our role in nature than the ‘automaton’ notion promulgated by classical physics." (Henry P Stapp, "Mindful Universe: Quantum Mechanics and the Participating Observer", 2007)

"Simpson’s Paradox can occur whenever data are aggregated. If data are collapsed across a subclassification (such as grades, race, or age), the overall difference observed may not represent what is going on. Standardization can help correct this, but nothing short of random assignment of individuals to groups will prevent the possibility of yet another subclassificatiion, as yet unidentified, changing things around again. But I believe that knowing of the possibility helps us, so that we can contain the enthusiasm of our impulsive first inferences." (Howard Wainer, "Graphic Discovery: A trout in the milk and other visuals" 2nd, 2008)

"Network stability may be a key element in the development of multilevel, nested networks. The formation of nested networks obviously requires at least a few contacts between the bottom networks. However, evolutionary selection requires the independence and at least temporary isolation of the bottom networks themselves. Weak links are probably the only tools for solving this apparent paradox." (Péter Csermely, "Weak Links: The Universal Key to the Stabilityof Networks and Complex Systems", 2009)