title: David Letterman

text: Beginning in May 1988, Letterman was stalked by Margaret Mary Ray, a woman with schizophrenia. She stole his Porsche, camped out on his tennis court, and repeatedly broke into his house. Her exploits drew national attention, with Letterman occasionally joking about her on his show, though he never named her. After she died by suicide at age 46 in October 1998, Letterman told "The New York Times" that he had great compassion for her. A spokesperson for Letterman said: "This is a sad ending to a confused life."


title: David Letterman

text: In 2005, another person was able to obtain a restraining order from a New Mexico judge, prohibiting Letterman from contacting her. She claimed he had sent her coded messages via his television program, causing her bankruptcy and emotional distress. Law professor Eugene Volokh called the case "patently frivolous".


title: David Letterman

text: Letterman is a car enthusiast and owns an extensive collection. In 2012, it was reported that the collection consisted of ten Ferraris, eight Porsches, four Austin-Healeys, two Honda motorcycles, a Chevy pickup, and one car each from automakers Mercedes-Benz, Jaguar, MG, Volvo, and Pontiac.


title: David Letterman

text: In his 2013 appearance on "Comedians in Cars Getting Coffee", part of Jerry Seinfeld's conversation with Letterman was filmed in Letterman's 1995 Volvo 960 station wagon, which is powered by a 380-horsepower racing engine. Paul Newman had the car built for Letterman.


title: David Letterman

text: Letterman shares a close relationship with the rock and roll band Foo Fighters since its appearance on his first show upon his return from heart surgery. The band appeared many times on the "Late Show", including a week-long stint in October 2014. While introducing the band's performance of "Miracle" on the show of October 17, 2014, Letterman told the story of how a souvenir video of himself and his four-year-old son learning to ski used the song as background music, unbeknownst to Letterman until he saw it. He stated: "This is the second song of theirs that will always have great, great meaning for me for the rest of my life". This was the first time the band had heard this story. Worldwide Pants co-produced Dave Grohl's "" TV series. "Letterman was the first person to get behind this project," Grohl said.


title: David Letterman

text: On September 7, 2007, Letterman visited his "alma mater", Ball State University in Muncie, Indiana, for the dedication of a communications facility named in his honor for his dedication to the university. The $21 million, David Letterman Communication and Media Building opened for the 2007 fall semester. Thousands of Ball State students, faculty, and local residents welcomed Letterman back to Indiana. Letterman's emotional speech touched on his struggles as a college student and his late father, and also included the "top ten good things about having your name on a building", finishing with "if reasonable people can put my name on a $21 million building, anything is possible." Over many years Letterman "has provided substantial assistance to [Ball State's] Department of Telecommunications, including an annual scholarship that bears his name."


title: David Letterman

text: At the same time, Indiana Governor Mitch Daniels gave Letterman a Sagamore of the Wabash award, which recognizes distinguished service to the state of Indiana.


title: David Letterman

text: In his capacities as a performer, producer, or as part of a writing team, Letterman is among the most nominated people in the history of the Emmy Awards, with 52 nominations, winning two Daytime Emmys and ten Primetime Emmys since 1981. He won four American Comedy Awards and in 2011 became the first recipient of the Johnny Carson Award for Comedic Excellence at The Comedy Awards.


title: David Letterman

text: Letterman was a recipient of the 2012 Kennedy Center Honors, where he was called "one of the most influential personalities in the history of television, entertaining an entire generation of late-night viewers with his unconventional wit and charm." On May 16, 2017, Letterman was named the next recipient of the Mark Twain Prize for American Humor, the award granted annually by the John F. Kennedy Center for the Performing Arts. He received the prize in a ceremony on October 22, 2017.


title: Sofia Boutella

text: Boutella was born in the Bab El Oued district of Algiers, Algeria, to an architect mother and a jazz musician father, Safy Boutella. Her brother, Seif, works as a visual effects artist in the entertainment industry. Her surname means "the men of the mountains". She was raised in a fairly secular household that cultivated artistic expression and creativity. Boutella described her childhood as a happy one, stating that she was "blessed to be born into a family that allowed me to express myself, to be myself and let out all sorts of colours that were living in my imagination and in my heart."


title: Sofia Boutella

text: With her family's encouragement, Boutella started classical dance education when she was five years old. In 1992, at the age of 10, she left Algeria with her family in the midst of the Algerian Civil War and moved to France. Shortly thereafter, she started rhythmic gymnastics, joining the French national team at age 18.


title: Sofia Boutella

text: Growing up in Paris, Boutella was exposed to many more forms of dance, particularly hip hop and street-dance, which intrigued her for offering more "freedom" compared to the more disciplined styles of ballet and gymnastics. She joined a group called the Vagabond Crew, which won the Battle of the Year in 2006, and participated in a spin-off group called "Chienne de Vie and Aphrodites".


title: Sofia Boutella

text: Her breakthrough as a dancer came in 2007, when she was picked for the Jamie King choreography for Nike Women's "Keep Up" campaign, serving as a role model of femininity and hip-hop. This was a major boost to her career and led to more work alongside stars like Madonna, in her Confessions Tour, and Rihanna. She credits her work with Madonna for helping her learn English.


title: Sofia Boutella

text: Boutella successfully auditioned for the Michael Jackson "This Is It" concerts but could not attend due to the extension of the Madonna tour, whose dates coincided with the Jackson tour. She was the main character in the music video for "Hollywood Tonight" by Michael Jackson in February 2011.


title: Sofia Boutella

text: Beginning at age 17, Boutella rehearsed with famed Spanish choreographer Blanca Li. She began dancing in film and television shows, as well as in commercials and concert tours.


title: Sofia Boutella

text: She played the lead character Eva in the drama film "StreetDance 2" (2012), the sequel to "StreetDance 3D" (2010).


title: Sofia Boutella

text: In 2014, after 12 years as a dancer, Boutella sought a career in acting. Initially, she purposefully avoided auditioning for lead roles, wishing to play supporting characters so as to learn from more experienced actors. In 2015, she appeared in her first major film, "", which jump-started her career as an actress. One year later, she appeared as the alien warrior Jaylah in "Star Trek Beyond", released on 22 July 2016.


title: Sofia Boutella

text: In 2017, she portrayed a French secret agent in the David Leitch film "Atomic Blonde", which also featured Charlize Theron, James McAvoy, John Goodman and Toby Jones. The same year, she played the titular role in "The Mummy", along with Tom Cruise, Russell Crowe and Annabelle Wallis.


title: Sofia Boutella

text: Beginning in 2018, Boutella's profile rose, and she began to appear in more central roles. That year, she appeared in the Gaspar Noé dark psychological horror film "Climax", starred alongside Michael B. Jordan and Michael Shannon in the HBO drama film "Fahrenheit 451", and portrayed French contract killer 'Nice' in the near-future action crime thriller "Hotel Artemis", alongside Jodie Foster, Jeff Goldblum, and Dave Bautista.


title: Sofia Boutella

text: In November 2021, Boutella was cast in the sci-fi adventure film "Rebel Moon" directed by Zack Snyder for Netflix.


title: Sofia Boutella

text: Boutella has cited Fred Astaire, Jean-Michel Basquiat, Daniel Day-Lewis and Bob Fosse as artistic influences.


title: Sofia Boutella

text: Although she has lived mostly in France since age 10, Boutella maintains strong ties to her Algerian roots and identity:


title: Scientific method

text: The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific method for additional detail.) It involves careful observation, applying rigorous skepticism about what is observed, given that cognitive assumptions can distort how one interprets the observation. It involves formulating hypotheses, via induction, based on such observations; the testability of hypotheses, experimental and the measurement-based statistical testing of deductions drawn from the hypotheses; and refinement (or elimination) of the hypotheses based on the experimental findings. These are "principles" of the scientific method, as distinguished from a definitive series of steps applicable to all scientific enterprises.


title: Scientific method

text: Although procedures vary from one field of inquiry to another, the underlying process is frequently the same from one field to another. The process in the scientific method involves making conjectures (hypothetical explanations), deriving predictions from the hypotheses as logical consequences, and then carrying out experiments or empirical observations based on those predictions. A hypothesis is a conjecture, based on knowledge obtained while seeking answers to the question. The hypothesis might be very specific, or it might be broad. Scientists then test hypotheses by conducting experiments or studies. A scientific hypothesis must be falsifiable, implying that it is possible to identify a possible outcome of an experiment or observation that conflicts with predictions deduced from the hypothesis; otherwise, the hypothesis cannot be meaningfully tested.


title: Scientific method

text: The purpose of an experiment is to determine whether observations agree with or conflict with the expectations deduced from a hypothesis. Experiments can take place anywhere from a garage to a remote mountaintop to CERN's Large Hadron Collider. There are difficulties in a formulaic statement of method, however. Though the scientific method is often presented as a fixed sequence of steps, it represents rather a set of general principles. Not all steps take place in every scientific inquiry (nor to the same degree), and they are not always in the same order.


title: Scientific method

text: Important debates in the history of science concern skepticism that anything can be known for sure (such as views of Francisco Sanches), rationalism (especially as advocated by René Descartes), inductivism, empiricism (as argued for by Francis Bacon, then rising to particular prominence with Isaac Newton and his followers), and hypothetico-deductivism, which came to the fore in the early 19th century.


title: Scientific method

text: The term "scientific method" emerged in the 19th century, when a significant institutional development of science was taking place and terminologies establishing clear boundaries between science and non-science, such as "scientist" and "pseudoscience", appeared. Throughout the 1830s and 1850s, at which time Baconianism was popular, naturalists like William Whewell, John Herschel, John Stuart Mill engaged in debates over "induction" and "facts" and were focused on how to generate knowledge. In the late 19th and early 20th centuries, a debate over realism vs. antirealism was conducted as powerful scientific theories extended beyond the realm of the observable.


title: Scientific method

text: The term "scientific method" came into popular use in the twentieth century; Dewey's 1910 book, "How We Think", inspired popular guidelines, popping up in dictionaries and science textbooks, although there was little consensus over its meaning. Although there was growth through the middle of the twentieth century, by the 1960s and 1970s numerous influential philosophers of science such as Thomas Kuhn and Paul Feyerabend had questioned the universality of the "scientific method" and in doing so largely replaced the notion of science as a homogeneous and universal method with that of it being a heterogeneous and local practice. In particular, Paul Feyerabend, in the 1975 first edition of his book "Against Method", argued against there being any universal rules of science; Popper 1963, Gauch 2003, and Tow 2010 disagree with Feyerabend's claim; problem solvers, and researchers are to be prudent with their resources during their inquiry.


title: Scientific method

text: Later stances include physicist Lee Smolin's 2013 essay "There Is No Scientific Method", in which he espouses two ethical principles, and historian of science Daniel Thurs's chapter in the 2015 book "Newton's Apple and Other Myths about Science", which concluded that the scientific method is a myth or, at best, an idealization. As myths are beliefs, they are subject to the narrative fallacy as Taleb points out. Philosophers Robert Nola and Howard Sankey, in their 2007 book "Theories of Scientific Method", said that debates over scientific method continue, and argued that Feyerabend, despite the title of "Against Method", accepted certain rules of method and attempted to justify those rules with a meta methodology.


title: Scientific method

text: Staddon (2017) argues it is a mistake to try following rules in the absence of an algorithmic scientific method; in that case, "science is best understood through examples". But algorithmic methods, such as "disproof of existing theory by experiment" have been used since Alhacen (1027) "Book of Optics", and Galileo (1638) "Two New Sciences", and "The Assayer" still stand as scientific method. They contradict Feyerabend's stance.


title: Scientific method

text: The ubiquitous element in the scientific method is empiricism. This is in opposition to stringent forms of rationalism: the scientific method embodies the position that reason alone cannot solve a particular scientific problem. A strong formulation of the scientific method is not always aligned with a form of empiricism in which the empirical data is put forward in the form of experience or other abstracted forms of knowledge; in current scientific practice, however, the use of scientific modelling and reliance on abstract typologies and theories is normally accepted. The scientific method counters claims that revelation, political or religious dogma, appeals to tradition, commonly held beliefs, common sense, or currently held theories pose the only possible means of demonstrating truth.


title: Scientific method

text: Different early expressions of empiricism and the scientific method can be found throughout history, for instance with the ancient Stoics, Epicurus, Alhazen, Avicenna, Roger Bacon, and William of Ockham. From the 16th century onwards, experiments were advocated by Francis Bacon, and performed by Giambattista della Porta, Johannes Kepler, and Galileo Galilei. There was particular development aided by theoretical works by Francisco Sanches, John Locke, George Berkeley, and David Hume.


title: Scientific method

text: A sea voyage from America to Europe afforded C. S. Peirce the distance to clarify his ideas, gradually resulting in the hypothetico-deductive model. Formulated in the 20th century, the model has undergone significant revision since first proposed (for a more formal discussion, see ).


title: Scientific method

text: The scientific method is the process by which science is carried out. As in other areas of inquiry, science (through the scientific method) can build on previous knowledge and develop a more sophisticated understanding of its topics of study over time. This model can be seen to underlie the scientific revolution.


title: Scientific method

text: The overall process involves making conjectures (hypotheses), deriving predictions from them as logical consequences, and then carrying out experiments based on those predictions to determine whether the original conjecture was correct. There are difficulties in a formulaic statement of method, however. Though the scientific method is often presented as a fixed sequence of steps, these actions are better considered as general principles. Not all steps take place in every scientific inquiry (nor to the same degree), and they are not always done in the same order. As noted by scientist and philosopher William Whewell (1794–1866), "invention, sagacity, [and] genius" are required at every step.


title: Scientific method

text: The question can refer to the explanation of a specific observation, as in "Why is the sky blue?" but can also be open-ended, as in "How can I design a drug to cure this particular disease?" This stage frequently involves finding and evaluating evidence from previous experiments, personal scientific observations or assertions, as well as the work of other scientists. If the answer is already known, a different question that builds on the evidence can be posed. When applying the scientific method to research, determining a good question can be very difficult and it will affect the outcome of the investigation.


title: Scientific method

text: A hypothesis is a conjecture, based on knowledge obtained while formulating the question, that may explain any given behavior. The hypothesis might be very specific; for example, Einstein's equivalence principle or Francis Crick's "DNA makes RNA makes protein", or it might be broad; for example, "unknown species of life dwell in the unexplored depths of the oceans". "See § Hypothesis development"


title: Scientific method

text: A statistical hypothesis is a conjecture about a given statistical population. For example, the population might be "people with a particular disease". One conjecture might be that a new drug will cure the disease in some of the people in that population, as in a clinical trial of the drug. A null hypothesis would conjecture that the statistical hypothesis is false; for example, that the new drug does nothing, and that any cure in the population would be caused by chance (a random variable).


title: Scientific method

text: An alternative to the null hypothesis, to be falsifiable, must say that a treatment program with the drug does better than chance. To test the statement "a treatment program with the drug does better than chance", an experiment is designed in which a portion of the population (the control group), is to be left untreated, while another, separate portion of the population is to be treated. t-Tests could then specify how large the treated groups, and how large the control groups are to be, in order to infer whether some course of treatment of the population has resulted in a cure of some of them, in each of the groups. The groups are examined, in turn by the researchers, in a protocol.


title: Scientific method

text: Strong inference could alternatively propose multiple alternative hypotheses embodied in randomized controlled trials, treatments A, B, C, ... , (say in a blinded experiment with varying dosages, or with lifestyle changes, and so forth) so as not to introduce confirmation bias in favor of a specific course of treatment. Ethical considerations could be used, to minimize the numbers in the untreated groups, e.g., use almost every treatment in every group, but excluding A, B, C, ..., respectively as controls.


title: Scientific method

text: The prediction step deduces the logical consequences of the hypothesis "before the outcome is known". These predictions are expectations for the results of testing. If the result is already known, it is evidence that is ready to be considered in acceptance or rejection of the hypothesis.


title: Scientific method

text: The evidence is also stronger if the actual result of the predictive test is not already known, as tampering with the test can be ruled out, as can hindsight bias (see postdiction). Ideally, the prediction must also distinguish the hypothesis from likely alternatives; if two hypotheses make the same prediction, observing the prediction to be correct is not evidence for either one over the other. (These statements about the relative strength of evidence can be mathematically derived using Bayes' Theorem).


title: Scientific method

text: The consequence, therefore, is to be stated at the same time or briefly after the statement of the hypothesis, but before the experimental result is known.


title: Scientific method

text: Likewise, the test protocol is to be stated before execution of the test. These requirements become precautions against tampering, and aid the reproducibility of the experiment.


title: Scientific method

text: Suitable tests of a hypothesis compare the expected values from the tests of that hypothesis with the actual results of those tests. Scientists (and other people) can then secure, or discard, their hypotheses by conducting suitable experiments.


title: Scientific method

text: An analysis determines, from the results of the experiment, the next actions to take. The expected values from the test of the alternative hypothesis are compared to the expected values resulting from the null hypothesis (that is, a prediction of no difference in the status quo). The difference between "expected versus actual" indicates which hypothesis better explains the resulting data from the experiment. In cases where an experiment is repeated many times, a statistical analysis such as a chi-squared test whether the null hypothesis is true, may be required.


title: Scientific method

text: Evidence from other scientists, and from experience are available for incorporation at any stage in the process. Depending on the complexity of the experiment, iteration of the process may be required to gather sufficient evidence to answer the question with confidence, or to build up other answers to highly specific questions, to answer a single broader question.


title: Scientific method

text: When the evidence has falsified the alternative hypothesis, a new hypothesis is required; if the evidence does not conclusively justify discarding the alternative hypothesis, other predictions from the alternative hypothesis might be considered. Pragmatic considerations, such as the resources available to continue inquiry, might guide the investigation's further course. When evidence for a hypothesis strongly supports that hypothesis, further questioning can follow, for insight into the broader inquiry under investigation.


title: Scientific method

text: The basic elements of the scientific method are illustrated by the following example (which occurred from 1944 to 1953) from the discovery of the structure of DNA:


title: Scientific method

text: The discovery became the starting point for many further studies involving the genetic material, such as the field of molecular genetics, and it was awarded the Nobel Prize in 1962. Each step of the example is examined in more detail later in the article.


title: Scientific method

text: The scientific method also includes other components required even when all the iterations of the steps above have been completed:


title: Scientific method

text: If an experiment cannot be repeated to produce the same results, this implies that the original results might have been in error. As a result, it is common for a single experiment to be performed multiple times, especially when there are uncontrolled variables or other indications of experimental error. For significant or surprising results, other scientists may also attempt to replicate the results for themselves, especially if those results would be important to their own work.


title: Scientific method

text: Replication has become a contentious issue in social and biomedical science where treatments are administered to groups of individuals. Typically an "experimental group" gets the treatment, such as a drug, and the "control group" gets a placebo. John Ioannidis in 2005 pointed out that the method being used has led to many findings that cannot be replicated.


title: Scientific method

text: The process of peer review involves evaluation of the experiment by experts, who typically give their opinions anonymously. Some journals request that the experimenter provide lists of possible peer reviewers, especially if the field is highly specialized. Peer review does not certify the correctness of the results, only that, in the opinion of the reviewer, the experiments themselves were sound (based on the description supplied by the experimenter). If the work passes peer review, which occasionally may require new experiments requested by the reviewers, it will be published in a peer-reviewed scientific journal. The specific journal that publishes the results indicates the perceived quality of the work.


title: Scientific method

text: Scientists typically are careful in recording their data, a requirement promoted by Ludwik Fleck (1896–1961) and others. Though not typically required, they might be requested to supply this data to other scientists who wish to replicate their original results (or parts of their original results), extending to the sharing of any experimental samples that may be difficult to obtain. "See §Communication and community."


title: Scientific method

text: Institutional researchers might acquire an instrument to institutionalize their tests. These instruments would use observations of the real world, which might agree with, or perhaps conflict with, their predictions deduced from their hypothesis. These institutions thereby reduce the research function to a cost/benefit, which is expressed as money, and the time and attention of the researchers to be expended, in exchange for a report to their constituents.


title: Scientific method

text: Current large instruments, such as CERN's Large Hadron Collider (LHC), or LIGO, or the National Ignition Facility (NIF), or the International Space Station (ISS), or the James Webb Space Telescope (JWST), entail expected costs of billions of dollars, and timeframes extending over decades. These kinds of institutions affect public policy, on a national or even international basis, and the researchers would require shared access to such machines and their adjunct infrastructure. "See Perceptual control theory, §Open-loop and closed-loop feedback"


title: Scientific method

text: There are different ways of outlining the basic method used for scientific inquiry. The scientific community and philosophers of science generally agree on the following classification of method components. These methodological elements and organization of procedures tend to be more characteristic of experimental sciences than social sciences. Nonetheless, the cycle of formulating hypotheses, testing and analyzing the results, and formulating new hypotheses, will resemble the cycle described below.


title: Scientific method

text: The scientific method is an iterative, cyclical process through which information is continually revised. It is generally recognized to develop advances in knowledge through the following elements, in varying combinations or contributions:


title: Scientific method

text: Each element of the scientific method is subject to peer review for possible mistakes. These activities do not describe all that scientists do but apply mostly to experimental sciences (e.g., physics, chemistry, biology, and psychology). The elements above are often taught in the educational system as "the scientific method".


title: Scientific method

text: The scientific method is not a single recipe: it requires intelligence, imagination, and creativity. In this sense, it is not a mindless set of standards and procedures to follow, but is rather an ongoing cycle, constantly developing more useful, accurate, and comprehensive models and methods. For example, when Einstein developed the Special and General Theories of Relativity, he did not in any way refute or discount Newton's "Principia". On the contrary, if the astronomically massive, the feather-light, and the extremely fast are removed from Einstein's theories – all phenomena Newton could not have observed – Newton's equations are what remain. Einstein's theories are expansions and refinements of Newton's theories and, thus, increase confidence in Newton's work.


title: Scientific method

text: An iterative, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:


title: Scientific method

text: While this schema outlines a typical hypothesis/testing method, many philosophers, historians, and sociologists of science, including Paul Feyerabend, claim that such descriptions of scientific method have little relation to the ways that science is actually practiced.


title: Scientific method

text: The scientific method depends upon increasingly sophisticated characterizations of the subjects of investigation. (The "subjects" can also be called or the "unknowns".) For example, Benjamin Franklin conjectured, correctly, that St. Elmo's fire was electrical in nature, but it has taken a long series of experiments and theoretical changes to establish this. While seeking the pertinent properties of the subjects, careful thought may also entail some definitions and observations; the observations often demand careful measurements and/or counting.


title: Scientific method

text: The systematic, careful collection of measurements or counts of relevant quantities is often the critical difference between pseudo-sciences, such as alchemy, and science, such as chemistry or biology. Scientific measurements are usually tabulated, graphed, or mapped, and statistical manipulations, such as correlation and regression, performed on them. The measurements might be made in a controlled setting, such as a laboratory, or made on more or less inaccessible or unmanipulatable objects such as stars or human populations. The measurements often require specialized scientific instruments such as thermometers, spectroscopes, particle accelerators, or voltmeters, and the progress of a scientific field is usually intimately tied to their invention and improvement.


title: Scientific method

text: Measurements in scientific work are also usually accompanied by estimates of their uncertainty. The uncertainty is often estimated by making repeated measurements of the desired quantity. Uncertainties may also be calculated by consideration of the uncertainties of the individual underlying quantities used. Counts of things, such as the number of people in a nation at a particular time, may also have an uncertainty due to data collection limitations. Or counts may represent a sample of desired quantities, with an uncertainty that depends upon the sampling method used and the number of samples taken.


title: Scientific method

text: Measurements demand the use of "operational definitions" of relevant quantities. That is, a scientific quantity is described or defined by how it is measured, as opposed to some more vague, inexact, or "idealized" definition. For example, electric current, measured in amperes, may be operationally defined in terms of the mass of silver deposited in a certain time on an electrode in an electrochemical device that is described in some detail. The operational definition of a thing often relies on comparisons with standards: the operational definition of "mass" ultimately relies on the use of an artifact, such as a particular kilogram of platinum-iridium kept in a laboratory in France.


title: Scientific method

text: The scientific definition of a term sometimes differs substantially from its natural language usage. For example, mass and weight overlap in meaning in common discourse, but have distinct meanings in mechanics. Scientific quantities are often characterized by their units of measure which can later be described in terms of conventional physical units when communicating the work.


title: Scientific method

text: New theories are sometimes developed after realizing certain terms have not previously been sufficiently clearly defined. For example, Albert Einstein's first paper on relativity begins by defining simultaneity and the means for determining length. These ideas were skipped over by Isaac Newton with, "I do not define , space, place and motion, as being well known to all." Einstein's paper then demonstrates that they (viz., absolute time and length independent of motion) were approximations. Francis Crick cautions us that when characterizing a subject, however, it can be premature to define something when it remains ill-understood. In Crick's study of consciousness, he actually found it easier to study awareness in the visual system, rather than to study free will, for example. His cautionary example was the gene; the gene was much more poorly understood before Watson and Crick's pioneering discovery of the structure of DNA; it would have been counterproductive to spend much time on the definition of the gene, before them.


title: Scientific method

text: The history of the discovery of the structure of DNA is a classic example of the elements of the scientific method: in 1950 it was known that genetic inheritance had a mathematical description, starting with the studies of Gregor Mendel, and that DNA contained genetic information (Oswald Avery's "transforming principle"). But the mechanism of storing genetic information (i.e., genes) in DNA was unclear. Researchers in Bragg's laboratory at Cambridge University made X-ray diffraction pictures of various molecules, starting with crystals of salt, and proceeding to more complicated substances. Using clues painstakingly assembled over decades, beginning with its chemical composition, it was determined that it should be possible to characterize the physical structure of DNA, and the X-ray images would be the vehicle. .."2. DNA-hypotheses"


title: Scientific method

text: The characterization element can require extended and extensive study, even centuries. It took thousands of years of measurements, from the Chaldean, Indian, Persian, Greek, Arabic, and European astronomers, to fully record the motion of planet Earth. Newton was able to include those measurements into the consequences of his laws of motion. But the perihelion of the planet Mercury's orbit exhibits a precession that cannot be fully explained by Newton's laws of motion (see diagram to the right), as Leverrier pointed out in 1859. The observed difference for Mercury's precession between Newtonian theory and observation was one of the things that occurred to Albert Einstein as a possible early test of his theory of General relativity. His relativistic calculations matched observation much more closely than did Newtonian theory. The difference is approximately 43 arc-seconds per century.


title: Scientific method

text: A hypothesis is a suggested explanation of a phenomenon, or alternately a reasoned proposal suggesting a possible correlation between or among a set of phenomena.


title: Scientific method

text: Normally hypotheses have the form of a mathematical model. Sometimes, but not always, they can also be formulated as existential statements, stating that some particular instance of the phenomenon being studied has some characteristic and causal explanations, which have the general form of universal statements, stating that every instance of the phenomenon has a particular characteristic.


title: Scientific method

text: Scientists are free to use whatever resources they have – their own creativity, ideas from other fields, inductive reasoning, Bayesian inference, and so on – to imagine possible explanations for a phenomenon under study. Albert Einstein once observed that "there is no logical bridge between phenomena and their theoretical principles." Charles Sanders Peirce, borrowing a page from Aristotle ("Prior Analytics", 2.25) described the incipient stages of inquiry, instigated by the "irritation of doubt" to venture a plausible guess, as "abductive reasoning". The history of science is filled with stories of scientists claiming a "flash of inspiration", or a hunch, which then motivated them to look for evidence to support or refute their idea. Michael Polanyi made such creativity the centerpiece of his discussion of methodology.


title: Scientific method

text: In general scientists tend to look for theories that are "elegant" or "beautiful". Scientists often use these terms to refer to a theory that is following the known facts but is nevertheless relatively simple and easy to handle. Occam's Razor serves as a rule of thumb for choosing the most desirable amongst a group of equally explanatory hypotheses.


title: Scientific method

text: To minimize the confirmation bias which results from entertaining a single hypothesis, strong inference emphasizes the need for entertaining multiple alternative hypotheses.


title: Scientific method

text: Linus Pauling proposed that DNA might be a triple helix. This hypothesis was also considered by Francis Crick and James D. Watson but discarded. When Watson and Crick learned of Pauling's hypothesis, they understood from existing data that Pauling was wrong. and that Pauling would soon admit his difficulties with that structure. So, the race was on to figure out the correct structure (except that Pauling did not realize at the time that he was in a race) "..3. DNA-predictions"


title: Scientific method

text: Any useful hypothesis will enable predictions, by reasoning including deductive reasoning. It might predict the outcome of an experiment in a laboratory setting or the observation of a phenomenon in nature. The prediction can also be statistical and deal only with probabilities.


title: Scientific method

text: It is essential that the outcome of testing such a prediction be currently unknown. Only in this case does a successful outcome increase the probability that the hypothesis is true. If the outcome is already known, it is called a consequence and should have already been considered while formulating the hypothesis.


title: Scientific method

text: If the predictions are not accessible by observation or experience, the hypothesis is not yet testable and so will remain to that extent unscientific in a strict sense. A new technology or theory might make the necessary experiments feasible. For example, while a hypothesis on the existence of other intelligent species may be convincing with scientifically based speculation, no known experiment can test this hypothesis. Therefore, science itself can have little to say about the possibility. In the future, a new technique may allow for an experimental test and the speculation would then become part of accepted science.


title: Scientific method

text: James D. Watson, Francis Crick, and others hypothesized that DNA had a helical structure. This implied that DNA's X-ray diffraction pattern would be 'x shaped'. This prediction followed from the work of Cochran, Crick and Vand (and independently by Stokes). The Cochran-Crick-Vand-Stokes theorem provided a mathematical explanation for the empirical observation that diffraction from helical structures produces x shaped patterns.


title: Scientific method

text: In their first paper, Watson and Crick also noted that the double helix structure they proposed provided a simple mechanism for DNA replication, writing, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material". " ..4. DNA-experiments"


title: Scientific method

text: Einstein's theory of general relativity makes several specific predictions about the observable structure of spacetime, such as that light bends in a gravitational field, and that the amount of bending depends in a precise way on the strength of that gravitational field. Arthur Eddington's observations made during a 1919 solar eclipse supported General Relativity rather than Newtonian gravitation.


title: Scientific method

text: Once predictions are made, they can be sought by experiments. If the test results contradict the predictions, the hypotheses which entailed them are called into question and become less tenable. Sometimes the experiments are conducted incorrectly or are not very well designed when compared to a crucial experiment. If the experimental results confirm the predictions, then the hypotheses are considered more likely to be correct, but might still be wrong and continue to be subject to further testing. The experimental control is a technique for dealing with observational error. This technique uses the contrast between multiple samples, or observations, or populations, under differing conditions, to see what varies or what remains the same. We vary the conditions for the acts of measurement, to help isolate what has changed. Mill's canons can then help us figure out what the important factor is. Factor analysis is one technique for discovering the important factor in an effect.


title: Scientific method

text: Depending on the predictions, the experiments can have different shapes. It could be a classical experiment in a laboratory setting, a double-blind study or an archaeological excavation. Even taking a plane from New York to Paris is an experiment that tests the aerodynamical hypotheses used for constructing the plane.


title: Scientific method

text: Scientists assume an attitude of openness and accountability on the part of those experimenting. Detailed record-keeping is essential, to aid in recording and reporting on the experimental results, and supports the effectiveness and integrity of the procedure. They will also assist in reproducing the experimental results, likely by others. Traces of this approach can be seen in the work of Hipparchus (190–120 BCE), when determining a value for the precession of the Earth, while controlled experiments can be seen in the works of al-Battani (853–929 CE) and Alhazen (965–1039 CE).


title: Scientific method

text: Watson and Crick showed an initial (and incorrect) proposal for the structure of DNA to a team from King's College London – Rosalind Franklin, Maurice Wilkins, and Raymond Gosling. Franklin immediately spotted the flaws which concerned the water content. Later Watson saw Franklin's detailed X-ray diffraction images which showed an X-shape and was able to confirm the structure was helical. This rekindled Watson and Crick's model building and led to the correct structure. "..1. DNA-characterizations"


title: Scientific method

text: The scientific method is iterative. At any stage, it is possible to refine its accuracy and precision, so that some consideration will lead the scientist to repeat an earlier part of the process. Failure to develop an interesting hypothesis may lead a scientist to re-define the subject under consideration. Failure of a hypothesis to produce interesting and testable predictions may lead to reconsideration of the hypothesis or of the definition of the subject. Failure of an experiment to produce interesting results may lead a scientist to reconsider the experimental method, the hypothesis, or the definition of the subject.


title: Scientific method

text: By 1027, Alhazen, based on his measurements of the refraction of light, was able to deduce that outer space was less dense than air, that is: "the body of the heavens is rarer than the body of air". In 1079 Ibn Mu'adh's "Treatise On Twilight" was able to infer that Earth's atmosphere was 50 miles thick, based on atmospheric refraction of the sun's rays.


title: Scientific method

text: Other scientists may start their own research and enter the process at any stage. They might adopt the characterization and formulate their own hypothesis, or they might adopt the hypothesis and deduce their own predictions. Often the experiment is not done by the person who made the prediction, and the characterization is based on experiments done by someone else. Published results of experiments can also serve as a hypothesis predicting their own reproducibility.


title: Scientific method

text: After considerable fruitless experimentation, being discouraged by their superior from continuing, and numerous false starts, Watson and Crick were able to infer the essential structure of DNA by concrete modeling of the physical shapes of the nucleotides which comprise it. They were guided by the bond lengths which had been deduced by Linus Pauling and by Rosalind Franklin's X-ray diffraction images. .."DNA Example"


title: Scientific method

text: Science is a social enterprise, and scientific work tends to be accepted by the scientific community when it has been confirmed. Crucially, experimental and theoretical results must be reproduced by others within the scientific community. Researchers have given their lives for this vision; Georg Wilhelm Richmann was killed by ball lightning (1753) when attempting to replicate the 1752 kite-flying experiment of Benjamin Franklin.


title: Scientific method

text: To protect against bad science and fraudulent data, government research-granting agencies such as the National Science Foundation, and science journals, including "Nature" and "Science", have a policy that researchers must archive their data and methods so that other researchers can test the data and methods and build on the research that has gone before. Scientific data archiving can be done at several national archives in the U.S. or the World Data Center.


title: Scientific method

text: Scientific inquiry generally aims to obtain knowledge in the form of testable explanations that scientists can use to predict the results of future experiments. This allows scientists to gain a better understanding of the topic under study, and later to use that understanding to intervene in its causal mechanisms (such as to cure disease). The better an explanation is at making predictions, the more useful it frequently can be, and the more likely it will continue to explain a body of evidence better than its alternatives. The most successful explanations – those which explain and make accurate predictions in a wide range of circumstances – are often called scientific theories.


title: Scientific method

text: Most experimental results do not produce large changes in human understanding; improvements in theoretical scientific understanding typically result from a gradual process of development over time, sometimes across different domains of science. Scientific models vary in the extent to which they have been experimentally tested and for how long, and in their acceptance in the scientific community. In general, explanations become accepted over time as evidence accumulates on a given topic, and the explanation in question proves more powerful than its alternatives at explaining the evidence. Often subsequent researchers re-formulate the explanations over time, or combined explanations to produce new explanations.


title: Scientific method

text: Tow sees the scientific method in terms of an evolutionary algorithm applied to science and technology. "See Ceteris paribus", and "Mutatis mutandis" "


title: Scientific method

text: Scientific knowledge is closely tied to empirical findings and can remain subject to falsification if new experimental observations are incompatible with what is found. That is, no theory can ever be considered final since new problematic evidence might be discovered. If such evidence is found, a new theory may be proposed, or (more commonly) it is found that modifications to the previous theory are sufficient to explain the new evidence. The strength of a theory relates to how long it has persisted without major alteration to its core principles ("see invariant explanations").


title: Scientific method

text: Theories can also become subsumed by other theories. For example, Newton's laws explained thousands of years of scientific observations of the planets . However, these laws were then determined to be special cases of a more general theory (relativity), which explained both the (previously unexplained) exceptions to Newton's laws and predicted and explained other observations such as the deflection of light by gravity. Thus, in certain cases independent, unconnected, scientific observations can be connected, unified by principles of increasing explanatory power.


title: Scientific method

text: Since new theories might be more comprehensive than what preceded them, and thus be able to explain more than previous ones, successor theories might be able to meet a higher standard by explaining a larger body of observations than their predecessors. For example, the theory of evolution explains the diversity of life on Earth, how species adapt to their environments, and many other patterns observed in the natural world; its most recent major modification was unification with genetics to form the modern evolutionary synthesis. In subsequent modifications, it has also subsumed aspects of many other fields such as biochemistry and molecular biology.


title: Scientific method

text: Scientific methodology often directs that hypotheses be tested in controlled conditions wherever possible. This is frequently possible in certain areas, such as in the biological sciences, and more difficult in other areas, such as in astronomy.


title: Scientific method

text: The practice of experimental control and reproducibility can have the effect of diminishing the potentially harmful effects of circumstance, and to a degree, personal bias. For example, pre-existing beliefs can alter the interpretation of results, as in confirmation bias; this is a heuristic that leads a person with a particular belief to see things as reinforcing their belief, even if another observer might disagree (in other words, people tend to observe what they expect to observe).


title: Scientific method

text: A historical example is the belief that the legs of a galloping horse are splayed at the point when none of the horse's legs touch the ground, to the point of this image being included in paintings by its supporters. However, the first stop-action pictures of a horse's gallop by Eadweard Muybridge showed this to be false, and that the legs are instead gathered together.


title: Scientific method

text: Another important human bias that plays a role is a preference for new, surprising statements (see "Appeal to novelty"), which can result in a search for evidence that the new is true. Poorly attested beliefs can be believed and acted upon via a less rigorous heuristic.


title: Scientific method

text: Goldhaber and Nieto published in 2010 the observation that if theoretical structures with "many closely neighboring subjects are described by connecting theoretical concepts, then the theoretical structure acquires a robustness which makes it increasingly hardthough certainly never impossibleto overturn". When a narrative is constructed its elements become easier to believe.


title: Scientific method

text: The classical model of scientific inquiry derives from Aristotle, who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy.


title: Scientific method

text: The hypothetico-deductive model or method is a proposed description of the scientific method. Here, predictions from the hypothesis are central: if you assume the hypothesis to be true, what consequences follow?


title: Scientific method

text: If a subsequent empirical investigation does not demonstrate that these consequences or predictions correspond to the observable world, the hypothesis can be concluded to be false.


title: Scientific method

text: In 1877, Charles Sanders Peirce (1839–1914) characterized inquiry in general not as the pursuit of truth "per se" but as the struggle to move from irritating, inhibitory doubts born of surprises, disagreements, and the like, and to reach a secure belief, the belief being that on which one is prepared to act. He framed scientific inquiry as part of a broader spectrum and as spurred, like inquiry generally, by actual doubt, not mere verbal or hyperbolic doubt, which he held to be fruitless. He outlined four methods of settling opinion, ordered from least to most successful:


title: Scientific method

text: Peirce held that slow, stumbling ratiocination can be dangerously inferior to instinct and traditional sentiment in practical matters, and that the scientific method is best suited to theoretical research, which in turn should not be trammeled by the other methods and practical ends; reason's "first rule" is that, in order to learn, one must desire to learn and, as a corollary, must not block the way of inquiry. The scientific method excels the others by being deliberately designed to arrive – eventually – at the most secure beliefs, upon which the most successful practices can be based. Starting from the idea that people seek not truth "per se" but instead to subdue irritating, inhibitory doubt, Peirce showed how, through the struggle, some can come to submit to the truth for the sake of belief's integrity, seek as truth the guidance of potential practice correctly to its given goal, and wed themselves to the scientific method.


title: Scientific method

text: For Peirce, rational inquiry implies presuppositions about truth and the real; to reason is to presuppose (and at least to hope), as a principle of the reasoner's self-regulation, that the real is discoverable and independent of our vagaries of opinion. In that vein, he defined truth as the correspondence of a sign (in particular, a proposition) to its object and, pragmatically, not as the actual consensus of some definite, finite community (such that to inquire would be to poll the experts), but instead as that final opinion which all investigators "would" reach sooner or later but still inevitably, if they were to push investigation far enough, even when they start from different points. In tandem he defined the real as a true sign's object (be that object a possibility or quality, or an actuality or brute fact, or a necessity or norm or law), which is what it is independently of any finite community's opinion and, pragmatically, depends only on the final opinion destined in a sufficient investigation. That is a destination as far, or near, as the truth itself to you or me or the given finite community. Thus, his theory of inquiry boils down to "Do the science." Those conceptions of truth and the real involve the idea of a community both without definite limits (and thus potentially self-correcting as far as needed) and capable of definite increase of knowledge. As inference, "logic is rooted in the social principle" since it depends on a standpoint that is, in a sense, unlimited.


title: Scientific method

text: Paying special attention to the generation of explanations, Peirce outlined the scientific method as coordination of three kinds of inference in a purposeful cycle aimed at settling doubts, as follows (in §III–IV in "A Neglected Argument" except as otherwise noted):


title: Scientific method

text: Frequently the scientific method is employed not only by a single person but also by several people cooperating directly or indirectly. Such cooperation can be regarded as an important element of a scientific community. Various standards of scientific methodology are used within such an environment.


title: Scientific method

text: Scientific journals use a process of "peer review", in which scientists' manuscripts are submitted by editors of scientific journals to (usually one to three, and usually anonymous) fellow scientists familiar with the field for evaluation. In certain journals, the journal itself selects the referees; while in others (especially journals that are extremely specialized), the manuscript author might recommend referees. The referees may or may not recommend publication, or they might recommend publication with suggested modifications, or sometimes, publication in another journal. This standard is practiced to various degrees by different journals and can have the effect of keeping the literature free of obvious errors and generally improve the quality of the material, especially in the journals that use the standard most rigorously. The peer-review process can have limitations when considering research outside the conventional scientific paradigm: problems of "groupthink" can interfere with open and fair deliberation of some new research.


title: Scientific method

text: Sometimes experimenters may make systematic errors during their experiments, veer from standard methods and practices (Pathological science) for various reasons, or, in rare cases, deliberately report false results. Occasionally because of this then, other scientists might attempt to repeat the experiments to duplicate the results.


title: Scientific method

text: Researchers sometimes practice scientific data archiving, such as in compliance with the policies of government funding agencies and scientific journals. In these cases, detailed records of their experimental procedures, raw data, statistical analyses, and source code can be preserved to provide evidence of the methodology and practice of the procedure and assist in any potential future attempts to reproduce the result. These procedural records may also assist in the conception of new experiments to test the hypothesis, and may prove useful to engineers who might examine the potential practical applications of a discovery.


title: Scientific method

text: When additional information is needed before a study can be reproduced, the author of the study might be asked to provide it. They might provide it, or if the author refuses to share data, appeals can be made to the journal editors who published the study or to the institution which funded the research.


title: Scientific method

text: Since a scientist can't record "everything" that took place in an experiment, facts selected for their apparent relevance are reported. This may lead, unavoidably, to problems later if some supposedly irrelevant feature is questioned. For example, Heinrich Hertz did not report the size of the room used to test Maxwell's equations, which later turned out to account for a small deviation in the results. The problem is that parts of the theory itself need to be assumed to select and report the experimental conditions. The observations are hence sometimes described as being 'theory-laden'.


title: Scientific method

text: Science applied to complex systems can involve elements such as transdisciplinarity, systems theory, control theory, and scientific modelling. The Santa Fe Institute studies such systems; Murray Gell-Mann interconnects these topics with message passing.


title: Scientific method

text: Some biological systems, such those involved in proprioception, have been fruitfully modeled by engineering techniques.


title: Scientific method

text: In general, the scientific method may be difficult to apply stringently to diverse, interconnected systems and large data sets. In particular, practices used within Big data, such as predictive analytics, may be considered to be at odds with the scientific method, as some of the data may have been stripped of the parameters which might be material in alternative hypotheses for an explanation; thus the stripped data would only serve to support the null hypothesis in the predictive analytics application. notes "a scientific discovery remains incomplete without considerations of the social practices that condition it".


title: Scientific method

text: Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science, and the ethic that is implicit in science. There are basic assumptions, derived from philosophy by at least one prominent scientist, that form the base of the scientific method – namely, that reality is objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world. These assumptions from methodological naturalism form a basis on which science may be grounded. Logical positivist, empiricist, falsificationist, and other theories have criticized these assumptions and given alternative accounts of the logic of science, but each has also itself been criticized.


title: Scientific method

text: Thomas Kuhn examined the history of science in his "The Structure of Scientific Revolutions", and found that the actual method used by scientists differed dramatically from the then-espoused method. His observations of science practice are essentially sociological and do not speak to how science is or can be practiced in other times and other cultures.


title: Scientific method

text: Norwood Russell Hanson, Imre Lakatos and Thomas Kuhn have done extensive work on the "theory-laden" character of observation. Hanson (1958) first coined the term for the idea that all observation is dependent on the conceptual framework of the observer, using the concept of gestalt to show how preconceptions can affect both observation and description. He opens Chapter 1 with a discussion of the Golgi bodies and their initial rejection as an artefact of staining technique, and a discussion of Brahe and Kepler observing the dawn and seeing a "different" sunrise despite the same physiological phenomenon. Kuhn and Feyerabend acknowledge the pioneering significance of Hanson's work.


title: Scientific method

text: Kuhn said the scientist generally has a theory in mind before designing and undertaking experiments to make empirical observations, and that the "route from theory to measurement can almost never be traveled backward". For Kuhn, this implies that how theory is tested is dictated by the nature of the theory itself, which led Kuhn to argue that "once it has been adopted by a profession ... no theory is recognized to be testable by any quantitative tests that it has not already passed" (revealing Kuhn's rationalist thinking style).


title: Scientific method

text: Paul Feyerabend similarly examined the history of science, and was led to deny that science is genuinely a methodological process. In his book "Against Method" he argues that scientific progress is "not" the result of applying any particular method. In essence, he says that for any specific method or norm of science, one can find a historic episode where violating it has contributed to the progress of science. Thus, if believers in the scientific method wish to express a single universally valid rule, Feyerabend jokingly suggests, it should be 'anything goes'. However, this is uneconomic. Criticisms such as Feyerabend's led to the strong programme, a radical approach to the sociology of science.


title: Scientific method

text: The postmodernist critiques of science have themselves been the subject of intense controversy. This ongoing debate, known as the science wars, is the result of conflicting values and assumptions between the postmodernist and realist camps. Whereas postmodernists assert that scientific knowledge is simply another discourse (note that this term has special meaning in this context) and not representative of any form of fundamental truth, realists in the scientific community maintain that scientific knowledge does reveal real and fundamental truths about reality. Many books have been written by scientists which take on this problem and challenge the assertions of the postmodernists while defending science as a legitimate method of deriving truth.


title: Scientific method

text: In anthropology and sociology, following the field research in an academic scientific laboratory by Latour and Woolgar, Karin Knorr Cetina has conducted a comparative study of two scientific fields (namely high energy physics and molecular biology) to conclude that the epistemic practices and reasonings within both scientific communities are different enough to introduce the concept of "epistemic cultures", in contradiction with the idea that a so-called "scientific method" is unique and a unifying concept. Comparing 'epistemic cultures' with Fleck 1935, Thought collectives, ("denkkollektiven"): "Entstehung und Entwicklung einer wissenschaftlichen Tatsache: Einfǖhrung in die Lehre vom Denkstil und Denkkollektiv"


title: Scientific method

text: Science is the process of gathering, comparing, and evaluating proposed models against observables. A model can be a simulation, mathematical or chemical formula, or set of proposed steps. Science is like mathematics in that researchers in both disciplines try to distinguish what is "known" from what is "unknown" at each stage of discovery. Models, in both science and mathematics, need to be internally consistent and also ought to be "falsifiable" (capable of disproof). In mathematics, a statement need not yet be proved; at such a stage, that statement would be called a conjecture. But when a statement has attained mathematical proof, that statement gains a kind of immortality which is highly prized by mathematicians, and for which some mathematicians devote their lives.


title: Scientific method

text: Mathematical work and scientific work can inspire each other. For example, the technical concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture has been proved using time as a mathematical concept in which objects can flow (see Ricci flow).


title: Scientific method

text: Nevertheless, the connection between mathematics and reality (and so science to the extent it describes reality) remains obscure. Eugene Wigner's paper, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", is a very well-known account of the issue from a Nobel Prize-winning physicist. In fact, some observers (including some well-known mathematicians such as Gregory Chaitin, and others such as Lakoff and Núñez) have suggested that mathematics is the result of practitioner bias and human limitation (including cultural ones), somewhat like the post-modernist view of science.


title: Scientific method

text: George Pólya's work on problem solving, the construction of mathematical proofs, and heuristic show that the mathematical method and the scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps.


title: Scientific method

text: In Pólya's view, "understanding" involves restating unfamiliar definitions in your own words, resorting to geometrical figures, and questioning what we know and do not know already; "analysis", which Pólya takes from Pappus, involves free and heuristic construction of plausible arguments, working backward from the goal, and devising a plan for constructing the proof; "synthesis" is the strict Euclidean exposition of step-by-step details of the proof; "review" involves reconsidering and re-examining the result and the path taken to it.


title: Scientific method

text: Building on Pólya's work, Imre Lakatos argued that mathematicians actually use contradiction, criticism, and revision as principles for improving their work. In like manner to science, where truth is sought, but certainty is not found, in "Proofs and Refutations", what Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that we should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample, i.e. an entity contradicting/not explained by the theorem is found, we adjust the theorem, possibly extending the domain of its validity. This is a continuous way our knowledge accumulates, through the logic and process of proofs and refutations. (However, if axioms are given for a branch of mathematics, this creates a logical system —Wittgenstein 1921 "Tractatus Logico-Philosophicus" 5.13; Lakatos claimed that proofs from such a system were tautological, i.e. internally logically true, by rewriting forms, as shown by Poincaré, who demonstrated the technique of transforming tautologically true forms (viz. the Euler characteristic) into or out of forms from homology, or more abstractly, from homological algebra.)


title: Scientific method

text: Lakatos proposed an account of mathematical knowledge based on Polya's idea of heuristics. In "Proofs and Refutations", Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He thought that mathematical 'thought experiments' are a valid way to discover mathematical conjectures and proofs.


title: Scientific method

text: Gauss, when asked how he came about his theorems, once replied "durch planmässiges Tattonieren" (through systematic palpable experimentation).


title: Scientific method

text: When the scientific method employs statistics as a key part of its arsenal, there are mathematical and practical issues that can have a deleterious effect on the reliability of the output of scientific methods. This is described in a popular 2005 scientific paper "Why Most Published Research Findings Are False" by John Ioannidis, which is considered foundational to the field of metascience. Much research in metascience seeks to identify poor use of statistics and improve its use. "See Preregistration (science)#Rationale"


title: Scientific method

text: The particular points raised are statistical ("The smaller the studies conducted in a scientific field, the less likely the research findings are to be true" and "The greater the flexibility in designs, definitions, outcomes, and analytical modes in a scientific field, the less likely the research findings are to be true.") and economical ("The greater the financial and other interests and prejudices in a scientific field, the less likely the research findings are to be true" and "The hotter a scientific field (with more scientific teams involved), the less likely the research findings are to be true.") Hence: "Most research findings are false for most research designs and for most fields" and "As shown, the majority of modern biomedical research is operating in areas with very low pre- and poststudy probability for true findings." However: "Nevertheless, most new discoveries will continue to stem from hypothesis-generating research with low or very low pre-study odds," which means that *new* discoveries will come from research that, when that research started, had low or very low odds (a low or very low chance) of succeeding. Hence, if the scientific method is used to expand the frontiers of knowledge, research into areas that are outside the mainstream will yield the newest discoveries. "See: Expected value of sample information, False positives and false negatives, Test statistic, and Type I and type II errors"


title: Scientific method

text: Somewhere between 33% and 50% of all scientific discoveries are estimated to have been "stumbled upon", rather than sought out. This may explain why scientists so often express that they were lucky. Louis Pasteur is credited with the famous saying that "Luck favours the prepared mind", but some psychologists have begun to study what it means to be 'prepared for luck' in the scientific context. Research is showing that scientists are taught various heuristics that tend to harness chance and the unexpected. This is what Nassim Nicholas Taleb calls "Anti-fragility"; while some systems of investigation are fragile in the face of human error, human bias, and randomness, the scientific method is more than resistant or tough – it actually benefits from such randomness in many ways (it is anti-fragile). Taleb believes that the more anti-fragile the system, the more it will flourish in the real world.


title: Scientific method

text: Psychologist Kevin Dunbar says the process of discovery often starts with researchers finding bugs in their experiments. These unexpected results lead researchers to try to fix what they "think" is an error in their method. Eventually, the researcher decides the error is too persistent and systematic to be a coincidence. The highly controlled, cautious, and curious aspects of the scientific method are thus what make it well suited for identifying such persistent systematic errors. At this point, the researcher will begin to think of theoretical explanations for the error, often seeking the help of colleagues across different domains of expertise.


title: Rhodesia

text: Rhodesia (, ), officially from 1970 the Republic of Rhodesia, was an unrecognised state in Southern Africa from 1965 to 1979, equivalent in territory to modern Zimbabwe. Rhodesia was the "de facto" successor state to the British colony of Southern Rhodesia, which had been self-governing since achieving responsible government in 1923. A landlocked nation, Rhodesia was bordered by South Africa to the south, Bechuanaland (later Botswana) to the southwest, Zambia (formerly Northern Rhodesia) to the northwest, and Mozambique (a Portuguese province until 1975) to the east. From 1965 to 1979, Rhodesia was one of two independent states on the African continent governed by a white minority of European descent and culture, the other being South Africa.


title: Rhodesia

text: In the late 19th century, the territory north of the Transvaal was chartered to the British South Africa Company, led by Cecil Rhodes. Rhodes and his Pioneer Column marched north in 1890, acquiring a huge block of territory that the company would rule until the early 1920s. In 1923, the company's charter was revoked, and Southern Rhodesia attained self-government and established a legislature. Between 1953 and 1963, Southern Rhodesia was joined with Northern Rhodesia and Nyasaland in the Federation of Rhodesia and Nyasaland.


title: Rhodesia

text: The rapid decolonisation of Africa in the late 1950s and early 1960s alarmed a significant proportion of Southern Rhodesia's white population. In an effort to delay the transition to black majority rule, the predominantly white Southern Rhodesian government issued its own Unilateral Declaration of Independence (UDI) from the United Kingdom on 11 November 1965. The new nation, identified simply as Rhodesia, initially sought recognition as an autonomous realm within the Commonwealth of Nations, but reconstituted itself as a republic in 1970. Two African nationalist parties, the Zimbabwe African People's Union (ZAPU) and Zimbabwe African National Union (ZANU), launched an armed insurgency against the government upon UDI, sparking the Rhodesian Bush War. Growing war weariness, diplomatic pressure, and an extensive trade embargo imposed by the United Nations prompted Rhodesian prime minister Ian Smith to concede to majority rule in 1978. However, elections and a multiracial provisional government, with Smith succeeded by moderate Abel Muzorewa, failed to appease international critics or halt the war. By December 1979 Muzorewa had secured an agreement with ZAPU and ZANU, allowing Rhodesia to briefly revert to colonial status pending new elections under British supervision. ZANU secured an electoral victory in 1980, and the country achieved internationally recognised independence in April 1980 as Zimbabwe.


title: Rhodesia

text: Rhodesia's largest cities were Salisbury (its capital city, now known as Harare) and Bulawayo. Prior to 1970, the unicameral Legislative Assembly was predominantly white, with a small number of seats reserved for black representatives. Following the declaration of a republic in 1970, this was replaced by a bicameral Parliament, with a House of Assembly and a Senate. The bicameral system was retained in Zimbabwe after 1980. Aside from its racial franchise, Rhodesia observed a fairly conventional Westminster system inherited from the United Kingdom, with a President acting as ceremonial head of state, while a Prime Minister headed the Cabinet as head of government.


title: Rhodesia

text: The official name of the country, according to the constitution adopted concurrently with the UDI in November 1965, was Rhodesia. This was not the case under British law, however, which considered the territory's legal name to be Southern Rhodesia, the name given to the country in 1898 during the British South Africa Company's administration of the Rhodesias, and retained by the self-governing colony of Southern Rhodesia after the end of company rule in 1923.


title: Rhodesia

text: This naming dispute dated back to October 1964, when Northern Rhodesia became independent from the UK and concurrently changed its name to Zambia. The Southern Rhodesian colonial government in Salisbury felt that in the absence of a "Northern" Rhodesia, the continued use of "Southern" was superfluous. It passed legislation to become simply Rhodesia, but the British government refused to approve this on the grounds that the country's name was defined by British legislation, so could not be altered by the colonial government. Salisbury went on using the shortened name in an official manner nevertheless, while the British government continued referring to the country as Southern Rhodesia. This situation continued throughout the UDI period. The shortened name was used by many people including the British government in the House of Commons.


title: Rhodesia

text: Until after the Second World War, the landlocked British possession of Southern Rhodesia was not developed as an indigenous African territory, but rather as a unique state that reflected its multiracial character. This situation certainly made it very different from other lands that existed under colonial rule, as many Europeans had arrived to make permanent homes, populating the towns as traders or settling to farm the most productive soils. In 1922, faced with the decision to join the Union of South Africa as a fifth province or accept nearly full internal autonomy, the electorate cast its vote against South African integration.


title: Rhodesia

text: In view of the outcome of the referendum, the territory was annexed by the United Kingdom on 12 September 1923. Shortly after annexation, on 1 October 1923, the first constitution for the new Colony of Southern Rhodesia came into force. Under this constitution, Southern Rhodesia was given the right to elect its own thirty-member legislature, premier, and cabinet—although the British Crown retained a formal veto over measures affecting natives and dominated foreign policy.


title: Rhodesia

text: Over the course of the next three decades, Southern Rhodesia experienced a degree of economic expansion and industrialisation almost unrivaled in sub-Saharan Africa. Its natural abundance of mineral wealth—including large deposits of chromium and manganese—contributed to the high rate of conventional economic growth. However, most colonies in Africa, even those rich in natural resources, experienced difficulty in achieving similar rates of development due to a shortage of technical and managerial skills. Small, rotating cadres of colonial civil servants who possessed little incentive to invest their skills in the local economy were insufficient to compensate for this disadvantage. Southern Rhodesia had negated the issue by importing a skilled workforce directly from abroad in the form of its disproportionately large European immigrant and expatriate population. For example, in 1951 over 90% of white Southern Rhodesians were engaged in what the British government classified as "skilled occupations", or professional and technical trades. This resulted in the establishment of a diversified economy with a strong manufacturing sector and iron and steel industries. As the white population increased, so too did capital imports, especially in the wake of the Second World War. The considerable investment made by European residents in the economy financed the development of Southern Rhodesia's export industries as well as the infrastructure necessary to integrate it further with international markets.


title: Rhodesia

text: In August 1953, Southern Rhodesia merged with Northern Rhodesia and Nyasaland, the two other British Central African territories, to form the Federation of Rhodesia and Nyasaland – a loose association that placed defence and economic direction under a central government but left many domestic affairs under the control of its constituent territories. As it began to appear that decolonisation was inevitable and indigenous black populations were pressing heavily for change, the federation was dissolved at the end of December 1963.


title: Rhodesia

text: Although prepared to grant formal independence to Southern Rhodesia (now Rhodesia), the British government had adopted a policy of "no independence before majority rule" (NIBMR), dictating that colonies with a significant, politically active population of European settlers would not receive independence except under conditions of majority rule. White Rhodesians balked at the premise of NIBMR; many felt they had a right to absolute political control, at least for the time being, despite their relatively small numbers. They were also disturbed by the chaos of the post-colonial political transitions occurring in other African nations at the time, such as the Democratic Republic of the Congo. A vocal segment of the white populace was open to the concept of gradually incorporating black Rhodesians into civil society and a more integrated political structure in theory, although not without qualification and equivocation. A greater degree of social and political equality, they argued, was acceptable once more black citizens had obtained higher educational and vocational standards. The second faction in the white community was wholly unwilling to concede the principle, much less the practice, of equality to the black population. Both groups remained opposed to majority rule in the near future. However, once Rhodesia had been introduced as a topic for discussion in international bodies, extension of the status quo became a matter of concern to the British government, which perceived the scrutiny as a serious embarrassment to the United Kingdom.


title: Rhodesia

text: After the federation was dissolved in December 1963, the then British Prime Minister, Sir Alec Douglas-Home, insisted that preconditions on independence talks hinge on what he termed the "five principles" – unimpeded progress to majority rule, assurance against any future legislation decidedly detrimental to black interests, "improvement in the political status" of local Africans, an end to official racial discrimination, and a political settlement that could be "acceptable to the whole population". Harold Wilson and his incoming Labour government took an even harder line on demanding that these points be legitimately addressed before a timetable for independence could be set.


title: Rhodesia

text: In 1964, growing white dissatisfaction with the ongoing negotiations played a major role in the ousting of Winston Field as Prime Minister of Southern Rhodesia. Field was succeeded by Ian Smith, chairman of the conservative Rhodesian Front Party and an outspoken critic of any immediate transition to majority rule. Smith, the colony's first Rhodesian-born leader, soon came to personify resistance to liberals in British government and those agitating for change at home. In September 1964, Smith visited Lisbon, where Portuguese prime minister António de Oliveira Salazar promised him "maximum support" if he should declare independence. Aside from a common interest in maintaining security ties in southern Africa, Salazar expressed a great deal of anger at Britain's refusal to support Portugal during the Indian annexation of Goa in 1961, admonishing Smith not to trust the British government. A Rhodesian Trade Office was opened in Lisbon in order to co-ordinate breaking the anticipated sanctions in the event of a unilateral declaration of independence later that year, which encouraged Smith not to compromise. In its turn, the Rhodesian Trade Office in Lisbon functioned as a "de facto" embassy and caused tension with London, which objected to Rhodesia conducting its own foreign policy. As land-locked Rhodesia bordered the Portuguese colony of Mozambique, Salazar's promise of "maximum support" from Portugal in breaking the anticipated sanctions gave Smith more grounds for self-confidence in his talks with London. Smith ruled out acceptance for all five of the British principles as they stood, implying instead that Rhodesia was already legally entitled to independence—a claim that was overwhelmingly endorsed by the predominantly white electorate in a referendum.


title: Rhodesia

text: Emboldened by the results of this referendum and the subsequent general election, the Rhodesian government threatened to declare independence without British consent. Harold Wilson countered by warning that such an irregular procedure would be considered treasonous, although he specifically rejected using armed force to quell a rebellion by English "kith and kin", or white Rhodesians of predominantly British descent and origin, many of whom still possessed sympathies and family ties to the United Kingdom. Wilson's refusal to consider a military option further encouraged Smith to proceed with his plans. Talks quickly broke down, and final efforts in October to achieve a settlement floundered; the Smith government remained unwilling to accept the five principles of independence, and the British government argued it would settle for nothing less.


title: Rhodesia

text: On 11 November 1965 the Cabinet of Rhodesia issued a unilateral declaration of independence (UDI). The UDI was immediately denounced as an "act of rebellion against the Crown" in the United Kingdom, and Wilson promised that the illegal action would be short-lived. However, given its self-governing status Rhodesia had no longer been within the United Kingdom's direct sphere of influence for some time, and the facade of continued British rule was rendered a constitutional fiction by UDI. In light of these circumstances, Wilson quickly realised his ability to assert direct leverage over the incumbent Rhodesian government was limited.


title: Rhodesia

text: On 12 October 1965, the United Nations General Assembly had noted the repeated threats of the Rhodesian authorities "to declare unilaterally the independence of Southern Rhodesia, in order to perpetuate minority rule", and called upon Wilson to use all means at his disposal (including military force) to prevent the Rhodesian Front from asserting independence. After UDI was proclaimed, UN officials branded the Rhodesian government as an "illegal racist minority regime" and called on member states to voluntarily sever economic ties with Rhodesia, recommending sanctions on petroleum products and military hardware. In December 1966, the UN further iterated that these sanctions were mandatory, and member states were explicitly barred from purchasing Rhodesian export goods, namely tobacco, chromium, copper, asbestos, sugar, and beef.


title: Rhodesia

text: The British government, having already adopted extensive sanctions of its own, dispatched a Royal Navy squadron to monitor oil deliveries in the port of Beira in Mozambique, from which a strategic pipeline ran to Umtali in Rhodesia. The warships were to deter "by force, if necessary, vessels reasonably believed to be carrying oil destined for (Southern) Rhodesia".


title: Rhodesia

text: Some Western nations, such as Switzerland, and West Germany, which were not UN member states, continued to conduct business openly with Rhodesia – the latter remained the Smith government's largest trading partner in Western Europe until 1973, when it was admitted to the UN. Japan remained the chief recipient of Rhodesian exports outside the African continent, and Iran also supplied oil to Rhodesia in violation of the embargo. Portugal served as a conduit for Rhodesian goods, which it exported through Mozambique with false certificates of origin. South Africa, too, refused to observe the UN sanctions. In 1971, the Byrd Amendment was passed in the United States, permitting American firms to go on importing Rhodesian chromium and nickel products as normal.


title: Rhodesia

text: Despite the poor showing of sanctions, Rhodesia found it nearly impossible to obtain diplomatic recognition abroad. In 1970, the United States declared it would not recognise UDI "under [any] circumstances". South Africa and Portugal, Rhodesia's largest trading partners, also refused to extend diplomatic recognition, and did not open embassies in the Rhodesian capital, Salisbury, preferring to conduct diplomatic activities through "accredited representatives". This allowed the South African and Portuguese governments to maintain they were continuing to respect British sovereignty while also accepting the practical authority of the Smith administration.


title: Rhodesia

text: Initially, the Rhodesian state retained its pledged loyalty to Queen Elizabeth II, recognising her as Queen of Rhodesia. When Smith and Deputy Prime Minister Clifford Dupont visited Sir Humphrey Gibbs, the Governor of Southern Rhodesia, to formally notify him of the UDI, Gibbs condemned it as an act of treason. After Smith formally announced the UDI on the radio, Governor Gibbs used his reserve power to dismiss Smith and his entire cabinet from office, on orders from the Colonial Office in Whitehall. However, Gibbs was unable to take any concrete actions to bring about a return to lawful colonial government. Rhodesian ministers simply ignored his notices, contending that UDI had made his office obsolete. Even so, Gibbs continued to occupy his official residence, Government House, in Salisbury until 1970, when he finally left Rhodesia, following the declaration of a republic. He had effectively been superseded before then; the Smith government stated that if the Queen did not appoint a Governor-General, it would name Dupont as "Officer Administering the Government". Smith had intended to have Dupont named Governor-General, but Queen Elizabeth II would not even consider this advice. With few exceptions, the international community backed Whitehall's assertion that Gibbs was the Queen's only legitimate representative, and hence the only lawful authority in Rhodesia.


title: Rhodesia

text: In September 1968, the Appellate Division of the High Court of Rhodesia ruled that Ian Smith's administration had become the "de jure" government of the country, not merely the "de facto" one. To support his decision, Chief Justice Sir Hugh Beadle used several statements made by Hugo Grotius, who maintained that there was no way that a nation could rightly claim to be governing a particular territory – if it was waging a war against that territory. Beadle argued that due to Britain's economic war against Rhodesia, she could not (at the same point) be described as "governing" Rhodesia. The ruling set the precedent that despite the UDI, the incumbent Smith government "could lawfully do anything its predecessors could lawfully have done".


title: Rhodesia

text: A Salisbury commission chaired by prominent lawyer W.R. Waley was appointed to study constitutional options open to the Rhodesian authorities as of April 1968, including on the topic of majority rule, but reopening negotiations with the British on a settlement was ruled out early on. The Waley Commission found that in practical as well legal terms, "Europeans must surrender any belief in permanent European domination", pointing out that minority rule was not permanently sustainable. However, Waley also testified that majority rule was not desirable immediately.


title: Rhodesia

text: Talks aimed at easing the differences between Rhodesia and the United Kingdom were carried out aboard Royal Navy vessels once in December 1966 and again in October 1968. Both efforts failed to achieve agreement, although Harold Wilson added a sixth principle to the five he had previously enunciated: "it would be necessary to ensure that, regardless of race, there was no oppression of the majority by the minority or of [any] minority by the majority." Rhodesian resolve stiffened following a failure to reach a new settlement, with more radical elements of the Rhodesian Front calling for a republican constitution.


title: Rhodesia

text: During a two-proposition referendum held in 1969, the proposal for severing all remaining ties to the British Crown passed by a majority of 61,130 votes to 14,327. Rhodesia declared itself a republic on 2 March 1970. Under the new constitution, a president served as ceremonial head of state, with the prime minister nominally reporting to him. Some in Rhodesian government had hoped in vain that the declaration of a republic would finally prompt other nations to grant recognition.


title: Rhodesia

text: The years following Rhodesia's UDI saw an unfolding series of economic, military, and political pressures placed on the country that eventually brought about majority rule, a totality of these factors rather than any one the reason for introducing change. In 2005, a conference at the London School of Economics that discussed Rhodesia's independence concluded that UDI was sparked by an existing racial conflict complicated by Cold War intrigues.


title: Rhodesia

text: Critics of UDI maintained that Ian Smith intended to safeguard the privileges of an entrenched colonial ruling class at the expense of the impoverished black population. Smith defended his actions by claiming that the black Rhodesian majority was too inexperienced at the time to participate in the complex administrative process of what was, by contemporary African standards, a reasonably industrialised state.


title: Rhodesia

text: At large, UDI further hardened the white population's attitudes towards majority rule and relations with the UK. A significant majority of white Rhodesian residents were either British immigrants or of British ancestry, and many held a special affection for the British Empire. However, the UK's refusal to grant them independence on their terms further confirmed their opposition to a political settlement on British terms, and fed their negative attitudes towards British interference in Rhodesian politics at large. In the years prior to UDI, white Rhodesians increasingly saw themselves as beleaguered and threatened, perpetually insecure and undermined by the metropole, unable to rely on anybody but themselves. The policy of "No independence before majority rule" transformed the white community's relationship with the UK and increased its suspicions of the British government's untrustworthiness and duplicity in colonial affairs, especially since the latter had adopted NIBMR as a formal policy - the very circumstance UDI was carried out to avoid, and which white Rhodesians had struggled to resist since the onset of decolonisation.


title: Rhodesia

text: Black nationalist parties reacted with outrage at UDI, with one ZANU official stating, "...for all those who cherish freedom and a meaningful life, UDI has set a collision course that cannot be altered. 11 November 1965 [has] marked the turning point of the struggle for freedom in that land from a constitutional and political one to primarily a military struggle." It would, however, be several years before the nationalists adopted armed struggle as their primary strategy for obtaining political power. Violent tactics at this time were intended to create opportunities for external intervention, either by the international community or the British government, rather than seriously undermine the Rhodesian security forces.


title: Rhodesia

text: Because Rhodesian exports were generally competitive and had previously been entitled to preferential treatment on the British market, the former colony did not recognise the need for escalating the pace of diversification before independence. Following the UDI, however, Rhodesia began to demonstrate that it had the potential to develop a greater degree of economic self-sufficiency. After the Rhodesian Front began introducing incentives accorded to domestic production, industrial output expanded dramatically. A rigid system of countermeasures enacted to combat sanctions succeeded in blunting their impact for at least a decade. Over the next nine years Rhodesian companies, spiting the freezing of their assets and blocking of overseas accounts, also perfected cunning techniques of sanctions evasion through both local and foreign subsidiaries, which operated on a clandestine trade network.


title: Rhodesia

text: From 1968 until 1970, there was virtually no further dialogue between Rhodesia and the UK. In a referendum in 1969, white voters approved a new constitution and the establishment of a republic, thereby severing Rhodesia's last links with the British Crown, duly declared in March 1970. This changed immediately after the election of Edward Heath, who reopened negotiations. Smith remained optimistic that Heath would do his utmost to remedy Anglo-Rhodesian relations, although disappointed that he continued to adhere publicly to the original "five principles" proposed by Alec Douglas-Home, now foreign secretary. In November 1971, Douglas-Home renewed contacts with Salisbury and announced a proposed agreement that would be satisfactory to both sides – it recognised Rhodesia's 1969 constitution as the legal frame of government, while agreeing that gradual legislative representation was an acceptable formula for unhindered advance to majority rule. Nevertheless, the new settlement, if approved, would also implement an immediate improvement in black political status, offer a means to terminate racial discrimination, and provide a solid guarantee against retrogressive constitutional amendments.


title: Rhodesia

text: Implementation of the proposed settlement hinged on popular acceptance, but the Rhodesian government consistently refused to submit it to a universal referendum. A twenty four-member commission headed by an eminent jurist, Lord Pearce, was therefore tasked with ascertaining public opinion on the subject. In 1972, the commission began interviewing interest groups and sampling opinions – although concern was expressed over the widespread apathy encountered. According to the commission, whites were in favour of the settlement, and Rhodesians of Coloured or Asian ancestry generally pleased, while the black response to the settlement's terms was resoundingly negative. As many as thirty black Rhodesian chiefs and politicians voiced their opposition, prompting Britain to withdraw from the proposals on the grounds of the commission's report.