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16,300 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,301 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,302 | 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, observi... | https://en.wikipedia.org/wiki?curid=26833 |
16,303 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,304 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,305 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,306 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,307 | 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 q... | https://en.wikipedia.org/wiki?curid=26833 |
16,308 | 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 inqu... | https://en.wikipedia.org/wiki?curid=26833 |
16,309 | 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: | https://en.wikipedia.org/wiki?curid=26833 |
16,310 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,311 | The scientific method also includes other components required even when all the iterations of the steps above have been completed: | https://en.wikipedia.org/wiki?curid=26833 |
16,312 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,313 | 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 m... | https://en.wikipedia.org/wiki?curid=26833 |
16,314 | 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, on... | https://en.wikipedia.org/wiki?curid=26833 |
16,315 | 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 shar... | https://en.wikipedia.org/wiki?curid=26833 |
16,316 | 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,... | https://en.wikipedia.org/wiki?curid=26833 |
16,317 | 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 af... | https://en.wikipedia.org/wiki?curid=26833 |
16,318 | 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 scien... | https://en.wikipedia.org/wiki?curid=26833 |
16,319 | 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: | https://en.wikipedia.org/wiki?curid=26833 |
16,320 | 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 m... | https://en.wikipedia.org/wiki?curid=26833 |
16,321 | 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 Einstei... | https://en.wikipedia.org/wiki?curid=26833 |
16,322 | An iterative, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding: | https://en.wikipedia.org/wiki?curid=26833 |
16,323 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,324 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,325 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,326 | 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 t... | https://en.wikipedia.org/wiki?curid=26833 |
16,327 | 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 t... | https://en.wikipedia.org/wiki?curid=26833 |
16,328 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,329 | 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 , ... | https://en.wikipedia.org/wiki?curid=26833 |
16,330 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,331 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,332 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,333 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,334 | 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 theoreti... | https://en.wikipedia.org/wiki?curid=26833 |
16,335 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,336 | To minimize the confirmation bias which results from entertaining a single hypothesis, strong inference emphasizes the need for entertaining multiple alternative hypotheses. | https://en.wikipedia.org/wiki?curid=26833 |
16,337 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,338 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,339 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,340 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,341 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,342 | 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-ex... | https://en.wikipedia.org/wiki?curid=26833 |
16,343 | 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 19... | https://en.wikipedia.org/wiki?curid=26833 |
16,344 | 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 t... | https://en.wikipedia.org/wiki?curid=26833 |
16,345 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,346 | 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 resul... | https://en.wikipedia.org/wiki?curid=26833 |
16,347 | 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 whi... | https://en.wikipedia.org/wiki?curid=26833 |
16,348 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,349 | 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 atmosp... | https://en.wikipedia.org/wiki?curid=26833 |
16,350 | 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 characterizatio... | https://en.wikipedia.org/wiki?curid=26833 |
16,351 | 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 ha... | https://en.wikipedia.org/wiki?curid=26833 |
16,352 | 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 ki... | https://en.wikipedia.org/wiki?curid=26833 |
16,353 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,354 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,355 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,356 | Tow sees the scientific method in terms of an evolutionary algorithm applied to science and technology. "See Ceteris paribus", and "Mutatis mutandis" " | https://en.wikipedia.org/wiki?curid=26833 |
16,357 | 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 prop... | https://en.wikipedia.org/wiki?curid=26833 |
16,358 | 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 New... | https://en.wikipedia.org/wiki?curid=26833 |
16,359 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,360 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,361 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,362 | 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 fal... | https://en.wikipedia.org/wiki?curid=26833 |
16,363 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,364 | 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 narrat... | https://en.wikipedia.org/wiki?curid=26833 |
16,365 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,366 | 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? | https://en.wikipedia.org/wiki?curid=26833 |
16,367 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,368 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,369 | 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 o... | https://en.wikipedia.org/wiki?curid=26833 |
16,370 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,371 | 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): | https://en.wikipedia.org/wiki?curid=26833 |
16,372 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,373 | 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 (e... | https://en.wikipedia.org/wiki?curid=26833 |
16,374 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,375 | 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 methodo... | https://en.wikipedia.org/wiki?curid=26833 |
16,376 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,377 | 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'... | https://en.wikipedia.org/wiki?curid=26833 |
16,378 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,379 | Some biological systems, such those involved in proprioception, have been fruitfully modeled by engineering techniques. | https://en.wikipedia.org/wiki?curid=26833 |
16,380 | 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 param... | https://en.wikipedia.org/wiki?curid=26833 |
16,381 | 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 real... | https://en.wikipedia.org/wiki?curid=26833 |
16,382 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,383 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,384 | 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, whic... | https://en.wikipedia.org/wiki?curid=26833 |
16,385 | 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, o... | https://en.wikipedia.org/wiki?curid=26833 |
16,386 | 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 disco... | https://en.wikipedia.org/wiki?curid=26833 |
16,387 | 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 sci... | https://en.wikipedia.org/wiki?curid=26833 |
16,388 | 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 ea... | https://en.wikipedia.org/wiki?curid=26833 |
16,389 | 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). | https://en.wikipedia.org/wiki?curid=26833 |
16,390 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,391 | 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. | https://en.wikipedia.org/wiki?curid=26833 |
16,392 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,393 | 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 ... | https://en.wikipedia.org/wiki?curid=26833 |
16,394 | 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 proo... | https://en.wikipedia.org/wiki?curid=26833 |
16,395 | Gauss, when asked how he came about his theorems, once replied "durch planmässiges Tattonieren" (through systematic palpable experimentation). | https://en.wikipedia.org/wiki?curid=26833 |
16,396 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,397 | 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 tr... | https://en.wikipedia.org/wiki?curid=26833 |
16,398 | 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... | https://en.wikipedia.org/wiki?curid=26833 |
16,399 | 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 coincidenc... | https://en.wikipedia.org/wiki?curid=26833 |
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