Suggestions for additions are welcome. This page is one of a series of sites related to uncertainty.
“The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.”
“Whereof one cannot speak, thereon one must remain silent.”
“I can live with doubt and uncertainty and not knowing. I think it's much more interesting to live not knowing than to have answers which might be wrong. I have approximate answers and possible beliefs and different degrees of uncertainty about different things, but I am not absolutely sure of anything and there are many things I don't know anything about, such as whether it means anything to ask why we're here. I don't have to know an answer. I don't feel frightened not knowing things, by being lost in a mysterious universe without any purpose, which is the way it really is as far as I can tell.”
“There was no way, without full understanding, that one could have confidence that conditions the next time might not produce erosion three times more severe than the time before. Nevertheless, officials fooled themselves into thinking they had such understanding and confidence, in spite of the peculiar variations from case to case. A mathematical model was made to calculate erosion. This was a model based not on physical understanding but on empirical curve fitting. To be more detailed, it was supposed a stream of hot gas impinged on the O-ring material, and the heat was determined at the point of stagnation (so far, with reasonable physical, thermodynamic laws). But to determine how much rubber eroded it was assumed this depended only on this heat by a formula suggested by data on a similar material. A logarithmic plot suggested a straight line, so it was supposed that the erosion varied as the .58 power of the heat, the .58 being determined by a nearest fit. At any rate, adjusting some other numbers, it was determined that the model agreed with the erosion (to depth of one-third the radius of the ring). There is nothing much so wrong with this as believing the answer! Uncertainties appear everywhere. How strong the gas stream might be was unpredictable, it depended on holes formed in the putty. Blow-by showed that the ring might fail even though not, or only partially eroded through. The empirical formula was known to be uncertain, for it did not go directly through the very data points by which it was determined. There were a cloud of points some twice above, and some twice below the fitted curve, so erosions twice predicted were reasonable from that cause alone. Similar uncertainties surrounded the other constants in the formula, etc., etc. When using a mathematical model careful attention must be given to uncertainties in the model.”
―Richard P. Feynman, Personal Observations on Reliability of Shuttle, Appendix F of the Rogers Commission Report on the Space Shuttle Challenger disaster
“There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
―Soren Kierkegaard
“It is evidently easier for the practitioner of natural science to recognize the difference between knowing and not knowing than this seems to be for the more abstract mathematician.”
―Ronald A. Fisher, Statistical Methods and Scientific Inference (third edition, 1973, page 20)
“It's not the figures lying that I'm worried about, it's the liars figuring.”
―anonymous (common attributions to Mark Twain are not substantiated)
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
“To learn which questions are unanswerable, and not to answer them: this skill is most needful in times of stress and darkness.”
―Ursula K. Le Guin, The Left Hand of Darkness
“Dubito, ergo cogito, ergo sum. [I doubt, therefore I think, therefore I am.]”
―Antoine Léonard Thomas, making a précis of Discours de le méthode by René Descartes
“Il n'est pas certain que tout soit incertain. [It is not certain that everything is uncertain.]”
“Blurry concepts influence one to focus, but postulated clarity influences arrogance.”
―Criss Jami, Salomé: In Every Inch In Every Mile
“You can only find truth with logic if you have already found truth without it.”
―G. K. Chesterton, Daily News, 25 February 1905, http://www.basicincome.com/bp/youcanonly.htm
“Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not "corrected" as a chance process unfolds, they are merely diluted.”
―Amos Tversky, Judgment Under Uncertainty: Heuristics and Biases
“...the ratings agencies' problem was in being unable or uninterested in appreciating the distinction between risk and uncertainty. ... The alchemy that the ratings agencies performed was to spin uncertainty into what looked and felt like risk. They took highly novel securities, subject to an enormous amount of systemic uncertainty, and claimed the ability to quantify just how risky they were. Not only that, but of all possible conclusions, they came to the astounding one that these investments were almost risk-free. ¶ Too many investors mistook these confident conclusions for accurate ones, and too few made backup plans in case things went wrong.”
―Nate Silver, The Signal and the Noise: Why So Many Predictions Fail―but Some Don't (2012)
“Knowledge is an unending adventure at the edge of uncertainty.”
―Jacob Bronowski
“The first principle is that you must not fool yourself—and you are the easiest person to fool.”
“Information is the resolution of uncertainty.”
―Claude Shannon
“Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.”
―Bertrand Russell in a 1929 lecture as cited by E.T. Bell's 1945 book The Development of Mathematics, (page 587, 2nd edition, McGraw-Hill)
“Croyez ceux qui cherchent la vérité, doutez de ceux qui la trouvent; doutez de tout, mais ne doutez pas de vous-même. [Believe those who seek the truth, doubt those who find it; doubt all, but do not doubt yourself.]”
―André Gide, Ainsi soit-il; ou, Les Jeux sont faits (1952, page 174)
“There is no falsification before the emergence of a better theory.”
―Imre Lakatos
“The power of the lawyer is in the uncertainty of the law.”
―Jeremy Bentham
“The men the American people admire most extravagantly are the most daring liars; the men they detest most violently are those who try to tell them the truth.”
―H.L. Mencken attributed
“No one ever went broke underestimating the intelligence of the American public.”
―H.L. Mencken, paraphrase of "No one in this world, so far as I know—and I have researched the records for years, and employed agents to help me—has ever lost money by underestimating the intelligence of the great masses of the plain people. Nor has anyone ever lost public office thereby." in the Chicago Tribune (19 September 1926)
“Humans are pattern-seeking story-telling animals, and we are quite adept at telling stories about patterns, whether they exist or not.”
“Smart people believe weird things because they are skilled at defending beliefs they arrived at for non-smart reasons.”
“We want to be open-minded enough to accept radical new ideas when they occasionally come along, but we don't want to be so open-minded that our brains fall out.”
“I’m a skeptic not because I do not want to believe, but because I want to know.”
“How you get to know is what I want to know.”
―Richard P. Feynman, The Meaning of It All: Thoughts of a Citizen-Scientist
“Le doute n’est pas une état bien agréable, mais l’assurance est un état ridicule. [Doubt is not a pleasant condition, but certainty is absurd.]”
“Knowing ignorance is strength. Ignoring knowledge is sickness.”
―Lao Tsu, Tao Te Ching
“Any measurement that you make without the knowledge of its uncertainty is completely meaningless.”
―Walter Lewin, MIT
“There is no such thing as a completely pure number, no such thing as a measurement that’s always perfect. ... [Even t]he act of counting is imprecise, and the degree of imprecision depends on what you’re counting and how you’re counting it.”
―Charles Seife, in chapter 5 of his book Proofiness
“...the difference between truth and falsehood did not seem important...”
―George Orwell, Nineteen Eighty-Four (Part Two, Section 5)
“Accepting that the world is full of uncertainty and ambiguity does not and should not stop people from being pretty sure about a lot of things.”
―Julian Baggini
“A decision made without taking uncertainty into account is barely worth calling a decision.”
―Richard Wilson, Edmund Crouch and Lauren Zeise, in a 1985 book chapter “Uncertainty in Risk Assessment” in Risk Quantitation and Regulatory Policy, Hoel et al. (eds.)
“Most of [physicists working in quantum mechanics in 1935] simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Nobody really doubts that [reality should be] something independent of the act of observation.”
“It must, in all justice, be admitted that never again will scientific life be as satisfying and serene as in days when determinism reigned supreme. In partial recompense for the tears we must shed and the toil we must endure is the satisfaction of knowing that we are treating significant problems in a more realistic and productive fashion.”
―Richard Bellman, Adaptive Control Processes: A Guided Tour (page 129f, 1961), An Introduction to Inequalities
“And if this calculus be condemned, then the whole of the sciences must also be condemned.”
―Henri Poincaré, referring to probability theory on page 186 of Science and Hypothesis (1905), translated from La Science et l'Hypothèse (1902)
“What do I know?”
―Michel de Montaigne, asking seriously the Pyrrhonist question “Que sçay-je?” [rendered in modern French as “Que sais-je?”]
“Thoroughly conscious ignorance...is a prelude to every real advance in knowledge.”
―James Clerk Maxwell, attributed by Stuart Firestein, and then widely attributed but without bibliographic reference. It is also anonymously claimed that Maxwell said “Statistical laws are not necessarily used as a result of our ignorance. Statistical laws can reflect how things really are. There are matters that can only be treated statistically.”
In his TED talk Pursuit of ignorance [https://www.youtube.com/watch?v=nq0_zGzSc8g], Firestein said “Knowledge is a big subject; ignorance is a bigger one.”
https://blog.explo.org/ignorance-is-more-bliss-its-scientific-necessity