“ “Beauty in mathematics is seeing the truth without effort.” ”—George Pólya, Hungarian Jewish mathematician. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory (1888-1985), cited in The study of education at Stanford: report to the university, Tom 8, Stanford University, 1969, p. 48.
[Risk intelligence] “it is the ability to estimate probabilities accurately, it’s about having the right amount of certainty to make educated guesses. That’s the simple definition. But this apparently simple skill turns out to be quite complex. It ends up being a rather deep thing about how to work on the basis of limited information and cope with an uncertain world, about knowing yourself and your limitations. (…)
Q: What mistakes do we make in assessing risks?
The need for closure is a really interesting one. If you have a great need for closure, it means you don’t like being in a state of uncertainty - you want an answer, any answer, even if it is the wrong one. On the other extreme, there is this need to avoid closure, where you are constantly seeking more information, so you get stuck in analysis paralysis.
Q: Can we increase our risk quotient?
Absolutely. One way is by being aware of different cognitive biases. Another is to play a personal prediction game. Bet against yourself and estimate probabilities of anything: whether your partner will get home before 6 o’clock, or whether it is going to rain, and keep track of them. Expert gamblers are constantly on the lookout for overconfidence, biases and so on. It is hard work, but it means they know themselves pretty well and they don’t have illusions. They know their weaknesses.” ”—Dylan Evans, British academic and author, visiting professor of psychology at the American University of Beirut, Lebanon. He has a PhD in philosophy from the London School of Economics, The man who gave us risk intelligence, New Scientist, 21 May 2012.
“ “The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.” ”—Henri Poincaré, French mathematician, theoretical physicist, engineer, and a philosopher of science (1854-1912), The Value of Science, Cosimo, Inc., 2007, p.8.
“ “The world is not a solid continent of facts sprinkled by a few lakes of uncertainties, but a vast ocean of uncertainties speckled by a few islands of calibrated and stabilized forms.” ”—Bruno Latour, French sociologist of science, anthropologist and an influential theorist in the field of Science and Technology Studies, Reassembling the Social: An Introduction to Actor-Network-Theory, Oxford University Press, 2007, p. 245.
“ “Every universe, our own included, begins in conversation. Every golem in the history of the world, from Rabbi Hanina’s delectable goat to the river-clay Frankenstein of Rabbi Judah Loew ben Bezalel, was summoned into existence through language, through murmuring, recital, and kabbalistic chitchat — was, literally, talked into life.” ”—Michael Chabon, American author, The Amazing Adventures of Kavalier and Clay, Random House, 2000.
“Science is about constructing visions of the world, about rearranging our conceptual structure, about creating new concepts which were not there before, and even more, about changing, challenging the a-priori that we have. So it’s nothing to do about the assembly of data and the way of organizing the assembly of data. It has everything to do about the way we think, and about our mental vision of the world. Science is a process in which we keep exploring ways of thinking, and changing our image of the world, our vision of the world, to find new ones that work a little bit better. (…) The past knowledge is always with us, and it’s our main ingredient for understanding. (…)
The deepest misunderstanding about science, which is the idea that science is about certainty. Science is not about certainty. Science is about finding the most reliable way of thinking, at the present level of knowledge. Science is extremely reliable; it’s not certain. In fact, not only it’s not certain, but it’s the lack of certainty that grounds it. Scientific ideas are credible not because they are sure, but because they are the ones that have survived all the possible past critiques, and they are the most credible because they were put on the table for everybody’s criticism.
The very expression ‘scientifically proven’ is a contradiction in terms. There is nothing that is scientifically proven. The core of science is the deep awareness that we have wrong ideas, we have prejudices. We have ingrained prejudices. In our conceptual structure for grasping reality there might be something not appropriate, something we may have to revise to understand better. So at any moment, we have a vision of reality that is effective, it’s good, it’s the best we have found so far. It’s the most credible we have found so far, its mostly correct. (…)
This continuous effort that is part of us to change our own way of thinking, to readapt, is a very part of our nature. We are not changing our mind away from nature; it is our natural history that continues to change that. (…)
It’s about overcoming our own ideas, and about going beyond common sense continuously. Science is a continuous challenge of common sense, and the core of science is not certainty, it’s continuous uncertainty. I would even say the joy of taking what we think, being aware that in everything we think, there are probably still an enormous amount of prejudices and mistakes, and try to learn to look a little bit larger, knowing that there is always a larger point of view that we’ll expect in the future.” ”—Carlo Rovelli, Italian theoretical physicist, working on quantum gravity and on foundations of spacetime physics. He is professor of physics at the University of the Mediterranean in Marseille, France and member of the Intitut Universitaire de France, cited in ☞ Science Is Not About Certainty. Science is about overcoming our own ideas and a continuous challenge of common sense, Lapidarium notes, May 24, 2012.
“ "The value of philosophy is, in fact, to be sought largely in its very uncertainty. The man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sense, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the co-operation or consent of his deliberate reason. To such a man the world tends to become definite, finite, obvious; common objects rouse no questions, and unfamiliar possibilities are contemptuously rejected. As soon as we begin to philosophize, on the contrary, we find that even the most everyday things lead to problems to which only very incomplete answers can be given.
Philosophy, though unable to tell us with certainty what is the true answer to the doubts it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what they may be; it removes the somewhat arrogant dogmatism of those who have never traveled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect.” ”—Bertrand Russell, British philosopher, logician, mathematician, historian, and social critic (1872-1970), The Problems of Philosophy(1912), Cosimo, Inc, 2010, p. 113-114.
“ "On the planet Earth, man had always assumed that he was more intelligent than dolphins because he had achieved so much - the wheel, New York, wars and so on - whilst all the dolphins had ever done was muck about in the water having a good time. But conversely, the dolphins had always believed that they were far more intelligent than man - for precisely the same reasons." ”—Douglas Adams, English writer and dramatist (1952-2001), The Hitchhiker’s Guide to the Galaxy, Pan Books, 1979, Chapter 23
#253 “At the core of all well-founded belief lies belief that is unfounded.”
#174. “I act with complete certainty. But this certainty is my own.”
#176. “Instead of “I know it” one may say in some cases “That’s how it is—rely upon it.” In some cases, however “I learned it years and years ago”; and sometimes: “I am sure it is so.”
#189. “At some point one has to pass from explanation to mere description.”
#191. “Well, if everything speaks for an hypothesis and nothing against it – is it then certainly true? One may designate it as such.—But does it certainly agree with reality, with the facts?—With this question you are already going round in a circle.”
#207. “Strange coincidence, that every man whose skull has been opened had a brain!” ”—Ludwig Wittgenstein, Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language (1889-1951), On Certainty (Über Gewissheit), J. & J. Harper Editions, New York, 1969.
“ "I am sitting with a philosopher in the garden; he says again and again "I know that that’s a tree", pointing to a tree that is near us. Someone else arrives and hears this, and I tell them: "This fellow isn’t insane. We are only doing philosophy.” ”—Ludwig Wittgenstein, Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language (1889-1951), On Certainty (Über Gewissheit), #467, J. & J. Harper Editions, New York, 1969.
Bruce Hood on The Self Illusion: How the Brain Creates Identity
“I think that both the “I” and the “me” are actually ever-changing narratives generated by our brain to provide a coherent framework to organize the output of all the factors that contribute to our thoughts and behaviors.
I think it helps to compare the experience of self to subjective contours – illusions such as the Kanizsa pattern where you see an invisible shape that is really defined entirely by the surrounding context. People understand that it is a trick of the mind but what they may not appreciate is that the brain is actually generating the neural activation as if the illusory shape was really there. In other words, the brain is hallucinating the experience. There are now many studies revealing that illusions generate brain activity as if they existed. They are not real but the brain treats them as if they were. (…)
Me is similarly constructed, though we may be more aware of the events that have shaped it over our lifetime. But neither is cast in stone and both are open to all manner of reinterpretation. As artists, illusionists, movie makers, and more recently experimental psychologists have repeatedly shown, conscious experience is highly manipulatable and context dependent. Our memories are also largely abstracted reinterpretations of events – we all hold distorted memories of past experiences. (…)
By rejecting the notion of a core self and considering how we are a multitude of competing urges and impulses, I think it is easier to understand why we suddenly go off the rails. It explains why we act, often unconsciously, in a way that is inconsistent with our self image – or the image of our self as we believe others see us.
That said, the self illusion is probably an inescapable experience we need for interacting with others and the world, and indeed we cannot readily abandon or ignore its influence, but we should be skeptical that each of us is the coherent, integrated entity we assume we are. (…)
There’s nothing at the center. We’re the product of the emergent property, I would argue, of the multitude of these processes that generate us.” ”—Bruce Hood Canadian-born experimental psychologist who specialises in developmental cognitive neuroscience, Director of the Bristol Cognitive Development Centre, based at the University of Bristol, cited in ☞ The Self Illusion: How the Brain Creates Identity, Lapidarium notes, May, 2012. (Illustration source)
“ "Eve and the apple was the first great step in experimental science." ”—James Bridie, was the pseudonym of a Scottish playwright, screenwriter and surgeon whose real name was Osborne Henry Mavor, Mr. Bolfry: a play in one act, Constable, 1948, p. 45.
“Paul King on what is the best explanation for identity
“From the perspective of neuroscience, personal identity is what happens when the brain forms of a model of the environment that includes a first-person perspective and narrative history.
Eric Kandel, lead editor of the textbook Principles of Neural Science, and winner of a Nobel Prize for work on the neural basis of memory, calls memory the “neural basis of individuation.” And it is. For without memory, we could not each carry around a unique sense of self, formed from a differentiated life history.
If everyone on the planet woke up one day with amnesia, human beings would be a herd of mostly undifferentiated people. Without the ability to distinguish one person from another, or remember unique histories or events, everyone becomes a vague blur of humanity.
In addition to our sense of unique personal history, the brain also maintains a model of other people. “Theory of mind" in cognitive science refers to the brain’s ability to model and track the goals, beliefs, and behavior patterns of other human beings around us in a social context. With a little introspection, this model of others can extend to ourself. As one comedian quipped: "How can I know what I think until I hear what I say?"
Because everyone in society carries around a model of themselves and the others they know, all the brains in human society collectively comprise a substrate for the distributed representation of human identity. Our identity is shaped not only by our own beliefs about ourselves, but by what others think of us as well. Social roles are collectively determined, and personality is shaped by how others treat us as well as are predisposition to a certain character and temperament.
And lastly, while personal identity feels unique, unified, and permanent, it is not. Identical twins are often confused. In institutions, people are identified by role (e.g. sales representative for the western region) while the actual person may change. And someone’s personality can change with mood. In children, we see personal identity form, and in senior dementia, we see it unravel.” ”—Paul King, visiting scholar at the Redwood Center for Theoretical Neuroscience at University of California, Berkeley, working on computational models of vision, What is the best explanation for identity (in a philosophical, neuroscientific, or psychological sense)?, Quora, Jan 18, 2012. (tnx wildcat2030)
“In the era of the Internet facts are not bricks but networks
“The existence of hyperlinks is enough to convince even the most stubborn positivist that there is always another side to the story. And on the web, fringe believers can always find each other and marinate in their own illusions. The “web world” is too big to ever know. There is always another link. In the era of the Internet, Weinbergerargues, facts are not bricks. They are networks. (…)
Human beings (or rather “Dasein,” “being-in-the-world”) are always thrown into a particular context, existing within already existing language structures and pre-determined meanings. In other words, the world is like the web, and we, Dasein, live inside the links. (…)
If knowledge has always been networked knowledge, than facts have never had stable containers. Most of the time, though, we more or less act as if they do. (…) Black boxes emerge out of actually-existing knowledge networks, stabilize for a time, and unravel, and our goal as thinkers and scholars ought to be understanding how these nodes emerge and disappear. (…)
Done well, digital realism can sensitize us to the fact that all networked knowledge systems eventually become brick walls, that these brick walls are maintained through technological, political, cultural, economic, and organizational forms of power. (…) Our job is to understand how the wall gets built, and how we might try to build it differently.” ”—C.W. Anderson, Ph.D, an assistant professor in the Department of Media Culture at the College of Staten Island (CUNY), researcher at the Columbia University Graduate School of Journalism, ☞ The Difference Between Online Knowledge and Truly Open Knowledge, The Atlantic, Feb 3, 2012.
“ "I think the Net generation is beginning to see knowledge in a way that is closer to the truth about knowledge. (…) Knowing looks less like capturing truths in books than engaging in never-settled networks of discussion and argument. (…) This new topology of knowledge reflects the topology of the Net. The Net (and especially the Web) is constructed quite literally out of links, each of which expresses some human interest. (…) And that’s the sense in which I think networked knowledge is more “natural.” (…)
The unique method of repeating kanji in a grid pattern in poem "Ame" (Rain).
As part of the wave of modernism that swept over all fields of art in the 20th century, poets boldly began to analyze language structurally instead of merely concentrating on its semantic content. (The Concrete Poetry of Niikuni Seiichi)
Concrete poetry or shape poetry is poetry in which the typographical arrangement of words is as important in conveying the intended effect as the conventional elements of the poem, such as meaning of words, rhythm, rhyme and so on. The French poet Pierre Guarnieri, collaborating with the Japanese poet Seiichi Niikuni, also used the term spatiality in relation to concrete poetry, implying that the white space between words also holds meaning. Poets emphasized that language is not only a means of communication, but that language also has a material dimension. (Wiki)”—Seiichi Niikuni, Japanese poet and painter. He was one of the foremost pioneers of the international avant-garde concrete poetry movement (1925-1977), "Ame" (Rain), Post-War Japanese Poetry, Penguin Books, 1972.
The language of thought drawing by Robert Horvitz
“The gap between outer langue and inner speech is greater than that between outer langue and outer speech. (…)
We are little gods in the world of inner speech. We are the only ones, we run the show, we are the boss. This world is almost a little insane, for it lacks the usual social controls, and we can be as bad or as goofy as we want. On the other hand inner speech does have a job to do, it has to steer us through the world. That function sets up outer limits, even though within those limits we have a free rein to construct this language as we like. (…)
Although inner speech is not idealism, in some ways it seems to be a more differentially defined universe than outer speech. Linguistic context is even more important than in outer speech. One reason is that meaning is so condensed on the two axes. But a second is that inner language is so pervaded with emotion. (…)
This language is so rooted in the unique self that an eavesdropper, could there be one, would not fully understand it. It has so much of one’s person in it, a listener would have to be another you to follow it. And if someone invented a window into consciousness, a mind-reading machine, that could invade one’s privacy, would they be able to understand the, now revealed, inner speech? I think not. They might be able to understand most of the words, but the non-linguistic or imagistic elements would be too much a personal script to follow. If this eavesdropper watched you, including your consciousness, for your whole life, had access to your memory and knew your way of combining non-linguistic representations with words, they might have your code, but this is another way of saying they would be another you. In practical terms inner speech would be inaccessible in its meaning even if it were accessible in its signifying forms. (…)
The importance of private language is that it sheds light on what a human being is. We are inherently private animals, and we become more so the more self-aware and internally communicative we are. This zone of privacy may well be the foundation for the moral (and legal) need people have for privacy. In any case the hidden individuality or uniqueness of each human being is closely related to the what the person says to him or her self. (…)
Inner speech is both the locus and platform for agency. (…) We choose internally in the zone of inner speech, and then we choose externally in the zone of practical action and the outer world. The first choice leads to the second choice. (…) We could make and break habits by first modelling them in our internal theater.” ”—Norbert Wiley, professor emeritus of Sociology at University of Illinois Urbana-Champaign, Illinois, Visiting Scholar at the University of California, Berkley. He is a prize-winning sociologist who has published on both the history and systematics of theory, cited in ☞ Do thoughts have a language of their own? The language of thought hypothesis, May, 2012.
“Abundance of all kinds will disappear, fade away,
Treasures and power will be swept away,
whole people will tremble,
Of the things of this world only two will remain,
Two only: poetry and goodness… and nothing else…” ”—Cyprian Norwid, Polish poet, dramatist, painter, and sculptor (1821-1883), Letter to Bronislaw Z., (1879), cited in Cyprian Norwid, Twayne Publishers, 1974, p. 63. (Illustration: Cyprian Norwid, Self-portrait)
“ “Mythmaking could never discover the origin and meaning of humanity” — and contemporary philosophy is also irrelevant, having “long ago abandoned the foundational questions about human existence.” The proper approach to answering these deep questions is the application of the methods of science, including archaeology, neuroscience and evolutionary biology. Also, we should study insects." ”—Edward O. Wilson, American biologist, researcher in sociobiology, biodiversity, theorist, naturalist and author, paraphrased by Paul Bloom in The Original Colonists, The New York Times, May 11, 2012.
Inside a mathematical proof lies literature. Some of the greatest mathematicians were also some of classical history’s most poetic storytellers
“Like novelists, mathematicians are creative authors. With diagrams, symbolism, metaphor, double entendre and elements of surprise, a good proof reads like a good story. (…) [Reviel] Netz reveals the stunning stylistic similarities between Hellenistic poetry and mathematical texts from the same era. (…) In the very layout, in the use of a particular formulaic language, in the structuring of the text (…) its success or failure depends entirely on features residing in the text itself. It is really an activity very powerfully concentrated around the manipulation of written documents, more perhaps than anywhere else in science, and comparable, then, to modern poetry. (…)
Metaphor is fairly standard in mathematics. Mathematics can only become truly interesting and original when it involves the operation of seeing something as something else – a pair of similarly looking triangles, say, as a site for an abstract proportion; a diagonal crossing through the set of all real numbers.” ”—Reviel Netz, Professor of Classics and Philosophy at Stanford University, Inside a mathematical proof lies literature, says Stanford’s Reviel Netz, Stanford University Report, May 7, 2012. See also: ☞ Oulipo - a group of writers interested in exploring the application of mathematical structures, patterns and algorithms to writing
“ "The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." ”—G. H. Hardy, was a prominent English mathematician, known for his achievements in number theory and mathematical analysis (1877-1947), A Mathematician’s Apology (1941)