Scientific method

Scientific method

Overview
Scientific method refers to a body of techniques
Scientific technique
A scientific technique is any systematic way of obtaining information about a scientific nature or to obtain a desired material or product.Scientific techniques can be divided in many different groups, e.g.:# Preparative techniques...

 for investigating phenomena
Phenomenon
A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'...

, acquiring new knowledge
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...

, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

 and measurable
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

 evidence subject to specific principles of reasoning. The Oxford English Dictionary
Oxford English Dictionary
The Oxford English Dictionary , published by the Oxford University Press, is the self-styled premier dictionary of the English language. Two fully bound print editions of the OED have been published under its current name, in 1928 and 1989. The first edition was published in twelve volumes , and...

 says that scientific method is: "a method of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses."

Although procedures vary from one field of inquiry to another, identifiable features distinguish scientific inquiry from other methods of obtaining knowledge.
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Encyclopedia
Scientific method refers to a body of techniques
Scientific technique
A scientific technique is any systematic way of obtaining information about a scientific nature or to obtain a desired material or product.Scientific techniques can be divided in many different groups, e.g.:# Preparative techniques...

 for investigating phenomena
Phenomenon
A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'...

, acquiring new knowledge
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...

, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

 and measurable
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

 evidence subject to specific principles of reasoning. The Oxford English Dictionary
Oxford English Dictionary
The Oxford English Dictionary , published by the Oxford University Press, is the self-styled premier dictionary of the English language. Two fully bound print editions of the OED have been published under its current name, in 1928 and 1989. The first edition was published in twelve volumes , and...

 says that scientific method is: "a method of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses."

Although procedures vary from one field of inquiry to another, identifiable features distinguish scientific inquiry from other methods of obtaining knowledge. Scientific researchers propose hypotheses as explanations of phenomena, and design experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

al studies to test these hypotheses via predictions which can be derived from them. These steps must be repeatable, to guard against mistake or confusion in any particular experimenter. Theories
Scientific theory
A scientific theory comprises a collection of concepts, including abstractions of observable phenomena expressed as quantifiable properties, together with rules that express relationships between observations of such concepts...

 that encompass wider domains of inquiry may bind many independently derived hypotheses together in a coherent, supportive structure. Theories, in turn, may help form new hypotheses or place groups of hypotheses into context.

Scientific inquiry is generally intended to be as objective
Objectivity (science)
Objectivity in science is a value that informs how science is practiced and how scientific truths are created. It is the idea that scientists, in attempting to uncover truths about the natural world, must aspire to eliminate personal biases, a priori commitments, emotional involvement, etc...

 as possible, to reduce biased interpretations of results. Another basic expectation is to document, archive
Scientific data archiving
Scientific data archiving refers to the long-term storage of scientific data and methods. The various scientific journals have differing policies regarding how much of their data and methods scientists are required to store in a public archive, and what is actually archived varies widely between...

 and share all data and methodology
Methodology
Methodology is generally a guideline for solving a problem, with specificcomponents such as phases, tasks, methods, techniques and tools . It can be defined also as follows:...

 so they are available for careful scrutiny by other scientists, giving them the opportunity to verify results by attempting to reproduce
Reproducibility
Reproducibility is the ability of an experiment or study to be accurately reproduced, or replicated, by someone else working independently...

 them. This practice, called full disclosure, also allows statistical measures of the reliability
Reliability (statistics)
In statistics, reliability is the consistency of a set of measurements or of a measuring instrument, often used to describe a test. Reliability is inversely related to random error.-Types:There are several general classes of reliability estimates:...

 of these data to be established.

Introduction to scientific method



Since Ibn al-Haytham (Alhazen, 965–1039), one of the key figures in the development of scientific method, according to Shmuel Sambursky, the emphasis has been on seeking truth:

The conjecture that "light travels through transparent bodies in straight lines only" was corroborated by Alhazen only after years of effort. His demonstration of the conjecture was to place a straight stick or a taut thread next to the light beam, to prove that light travels in a straight line.

Scientific methodology has been practiced in some form for at least one thousand years. There are difficulties in a formulaic statement of method, however. As William Whewell
William Whewell
William Whewell was an English polymath, scientist, Anglican priest, philosopher, theologian, and historian of science. He was Master of Trinity College, Cambridge.-Life and career:Whewell was born in Lancaster...

 (1794–1866) noted in his History of Inductive Science (1837) and in Philosophy of Inductive Science (1840), "invention, sagacity, genius" are required at every step in scientific method. It is not enough to base scientific method on experience
Empiricism
Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...

 alone; multiple steps are needed in scientific method, ranging from our experience to our imagination, back and forth.

In the 20th century, a hypothetico-deductive model
Hypothetico-deductive model
The hypothetico-deductive model or method, first so-named by William Whewell, is a proposed description of scientific method. According to it, scientific inquiry proceeds by formulating a hypothesis in a form that could conceivably be falsified by a test on observable data...

 for scientific method was formulated (for a more formal discussion, see below):
This model underlies the scientific revolution
Scientific revolution
The Scientific Revolution is an era associated primarily with the 16th and 17th centuries during which new ideas and knowledge in physics, astronomy, biology, medicine and chemistry transformed medieval and ancient views of nature and laid the foundations for modern science...

. One thousand years ago, Alhazen demonstrated the importance of steps 1 and 4. also showed the importance of step 4 (also called Experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

) in Two New Sciences
Two New Sciences
The Discourses and Mathematical Demonstrations Relating to Two New Sciences was Galileo's final book and a sort of scientific testament covering much of his work in physics over the preceding thirty years.After his Dialogue Concerning the Two Chief World Systems, the Roman Inquisition had banned...

. One possible sequence in this model would be 1, 2, 3, 4. If the outcome of 4 holds, and 3 is not yet disproven, you may continue with 3, 4, 1, and so forth; but if the outcome of 4 shows 3 to be false, you will have to go back to 2 and try to invent a new 2, deduce a new 3, look for 4, and so forth.

Note that this method can never absolutely verify (prove the truth of) 2. It can only falsify
Falsifiability
Falsifiability or refutability of an assertion, hypothesis or theory is the logical possibility that it can be contradicted by an observation or the outcome of a physical experiment...

2. (This is what Einstein meant when he said, "No amount of experimentation can ever prove me right; a single experiment can prove me wrong.")
However, as pointed out by Carl Hempel (1905–1997) this simple view of scientific method is incomplete; the formulation of the conjecture might itself be the result of inductive reasoning
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

. Thus the likelihood of the prior observation being true is statistical in nature and would strictly require a Bayesian analysis. To overcome this uncertainty, experimental scientists must formulate a crucial experiment, in order for it to corroborate a more likely hypothesis.

In the 20th century, Ludwik Fleck
Ludwik Fleck
Ludwik Fleck was a Polish Israeli medical doctor and biologist who developed in the 1930s the concept of Denkkollektiv...

 (1896–1961) and others argued that scientists need to consider their experiences more carefully, because their experience may be biased, and that they need to be more exact when describing their experiences.

DNA example

Four basic elements of scientific method are illustrated by the following example from the discovery of the structure of DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...

:
  • DNA characterization: Although DNA had been identified as at least one and possibly the only genetic substance by Avery, Macleod and McCarty at the Rockefeller Institute in 1944, the mechanism was still unclear to anyone in 1950.
  • DNA hypotheses: Crick
    Francis Crick
    Francis Harry Compton Crick OM FRS was an English molecular biologist, biophysicist, and neuroscientist, and most noted for being one of two co-discoverers of the structure of the DNA molecule in 1953, together with James D. Watson...

     and Watson
    James D. Watson
    James Dewey Watson is an American molecular biologist, geneticist, and zoologist, best known as one of the co-discoverers of the structure of DNA in 1953 with Francis Crick...

     hypothesized that the genetic material had a physical basis that was helical.
  • DNA prediction: From earlier work on tobacco mosaic virus
    Tobacco mosaic virus
    Tobacco mosaic virus is a positive-sense single stranded RNA virus that infects plants, especially tobacco and other members of the family Solanaceae. The infection causes characteristic patterns on the leaves . TMV was the first virus to be discovered...

    , Watson was aware of the significance of Crick's formulation of the transform of a helix. Thus he was primed to recognize the significance of the X-shape in photo 51
    Photo 51
    Photo 51 is the nickname given to an X-ray diffraction image of DNA taken by Rosalind Franklin in 1952 that was critical evidence in identifying the structure of DNA. The photo was taken by Franklin while working at King's College London in Sir John Randall's group.James D...

    , the remarkable photograph of the X-ray diffraction image of DNA taken by Rosalind Franklin
    Rosalind Franklin
    Rosalind Elsie Franklin was a British biophysicist and X-ray crystallographer who made critical contributions to the understanding of the fine molecular structures of DNA, RNA, viruses, coal and graphite...

    .
  • DNA experiment: Watson saw photo 51.


The examples are continued in "Evaluations and iterations" with DNA-iterations.

Truth and belief



In the same way that Alhazen sought truth during his pioneering studies in optics 1000 years ago, arriving at the truth is the goal of a scientific inquiry.

Beliefs and biases


Belief can alter observation; human confirmation bias
Confirmation bias
Confirmation bias is a tendency for people to favor information that confirms their preconceptions or hypotheses regardless of whether the information is true.David Perkins, a geneticist, coined the term "myside bias" referring to a preference for "my" side of an issue...

 is a heuristic
Heuristic
Heuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...

 that leads a person with a particular belief to see things as reinforcing their belief, even if another observer might disagree. Researchers have often noted that first observations are often somewhat imprecise, whereas the second and third were "adjusted to the facts". Eventually, factors such as openness to experience
Openness to experience
Openness to experience is one of the domains which are used to describe human personality in the Five Factor Model Openness involves active imagination, aesthetic sensitivity, attentiveness to inner feelings, preference for variety, and intellectual curiosity. A great deal of psychometric research...

, self-esteem
Self-esteem
Self-esteem is a term in psychology to reflect a person's overall evaluation or appraisal of his or her own worth. Self-esteem encompasses beliefs and emotions such as triumph, despair, pride and shame: some would distinguish how 'the self-concept is what we think about the self; self-esteem, the...

, time, and comfort can produce a readiness for new perception.


Needham's
Joseph Needham
Noel Joseph Terence Montgomery Needham, CH, FRS, FBA , also known as Li Yuese , was a British scientist, historian and sinologist known for his scientific research and writing on the history of Chinese science. He was elected a fellow of the Royal Society in 1941, and as a fellow of the British...

 Science and Civilization in China uses the 'flying gallop' image as an example of observation bias: In these images, the legs of a galloping horse are shown splayed, while the first stop-action pictures of a horse's gallop by Eadweard Muybridge
Eadweard Muybridge
Eadweard J. Muybridge was an English photographer who spent much of his life in the United States. He is known for his pioneering work on animal locomotion which used multiple cameras to capture motion, and his zoopraxiscope, a device for projecting motion pictures that pre-dated the flexible...

 showed this to be false. In a horse's gallop, at the moment that no hoof touches the ground, a horse's legs are gathered together—not splayed. Earlier paintings show an incorrect flying gallop observation.

This image illustrates Ludwik Fleck's
Ludwik Fleck
Ludwik Fleck was a Polish Israeli medical doctor and biologist who developed in the 1930s the concept of Denkkollektiv...

 suggestion that people be cautious lest they observe what is not so; people often observe what they expect to observe. Until shown otherwise; their beliefs affect their observations (and, therefore, any subsequent actions which depend on those observations, in a self-fulfilling prophecy
Self-fulfilling prophecy
A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true, by the very terms of the prophecy itself, due to positive feedback between belief and behavior. Although examples of such prophecies can be found in literature as far back as ancient Greece and...

). This is one of the reasons (mistake, confusion, inadequate instruments, etc. are others) why scientific methodology directs that hypotheses
Hypothesis
A hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

 be tested in controlled
Scientific control
Scientific control allows for comparisons of concepts. It is a part of the scientific method. Scientific control is often used in discussion of natural experiments. For instance, during drug testing, scientists will try to control two groups to keep them as identical and normal as possible, then...

 conditions which can be reproduced
Reproducibility
Reproducibility is the ability of an experiment or study to be accurately reproduced, or replicated, by someone else working independently...

 by others. The scientific community's
Scientific community
The scientific community consists of the total body of scientists, its relationships and interactions. It is normally divided into "sub-communities" each working on a particular field within science. Objectivity is expected to be achieved by the scientific method...

 pursuit of experimental control and reproducibility, diminishes the effects of cognitive biases.

Certainty and myth


Any scientific theory is closely tied to empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

 findings, and always remains subject to falsification
Falsifiability
Falsifiability or refutability of an assertion, hypothesis or theory is the logical possibility that it can be contradicted by an observation or the outcome of a physical experiment...

 if new experimental observation incompatible with it is found. That is, no theory can ever be seriously considered certain
Certainty
Certainty can be defined as either:# perfect knowledge that has total security from error, or# the mental state of being without doubtObjectively defined, certainty is total continuity and validity of all foundational inquiry, to the highest degree of precision. Something is certain only if no...

 as new evidence falsifying it can be discovered. Most scientific theories don't result in large changes in human understanding. Improvements in theoretical scientific understanding is usually the result of a gradual synthesis of the results of different experiments, by various researchers, across different domains of science. Theories vary in the extent to which they have been experimentally tested and for how long, and in their acceptance in the scientific community.

In contrast to the always-provisional status of scientific theory, a myth can be believed and acted upon, or depended upon, irrespective of its truth. Imre Lakatos
Imre Lakatos
Imre Lakatos was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his...

 has noted that once a narrative is constructed its elements become easier to believe (this is called the narrative fallacy). That is, theories become accepted by a scientific community as evidence for the theory is presented, and as presumptions that are inconsistent with the evidence are falsified. -- The difference between a theory and a myth reflects a preference for a posteriori versus a priori knowledge. --

Thomas Brody notes that confirmed theories are subject to subsumption by other theories, as special cases of a more general theory. For example, thousands of years of scientific observations of the planets were explained by Newton's laws. Thus the body of independent, unconnected, scientific observation can diminish. Yet there is a preference in the scientific community for new, surprising statements, and the search for evidence that the new is true. additionally state that "If many closely neighboring subjects are described by connecting theoretical concepts, then a theoretical structure acquires a robustness which makes it increasingly hard —though certainly never impossible— to overturn."

Elements of scientific method


There are different ways of outlining the basic method used for scientific inquiry. The scientific community
Scientific community
The scientific community consists of the total body of scientists, its relationships and interactions. It is normally divided into "sub-communities" each working on a particular field within science. Objectivity is expected to be achieved by the scientific method...

 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 natural science
Natural science
The natural sciences are branches of science that seek to elucidate the rules that govern the natural world by using empirical and scientific methods...

s than social sciences. Nonetheless, the cycle of formulating hypotheses, testing and analyzing the results, and formulating new hypotheses, will resemble the cycle described below.
Four essential elements of a scientific method are iteration
Iteration
Iteration means the act of repeating a process usually with the aim of approaching a desired goal or target or result. Each repetition of the process is also called an "iteration," and the results of one iteration are used as the starting point for the next iteration.-Mathematics:Iteration in...

s, recursion
Recursion
Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from...

s, interleaving
Interleaving
In computer science and telecommunication, interleaving is a way to arrange data in a non-contiguous way to increase performance.It is typically used:* In error-correction coding, particularly within data transmission, disk storage, and computer memory....

s, or orderings
Partially ordered set
In mathematics, especially order theory, a partially ordered set formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the...

 of the following:
  • Characterizations (observations, definitions, and measurements of the subject of inquiry)
  • Hypotheses (theoretical, hypothetical explanation
    Explanation
    An explanation is a set of statements constructed to describe a set of facts which clarifies the causes, context, and consequencesof those facts....

    s of observations and measurements of the subject)
  • Predictions (reasoning including logic
    Logic
    In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

    al deduction
    Deductive reasoning
    Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

     from the hypothesis
    Hypothesis
    A hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

     or theory
    Theory
    The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...

    )
  • Experiments (tests
    Experiment
    An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

     of all of the above)


Each element of a scientific method is subject to peer review
Peer review
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...

 for possible mistakes. These activities do not describe all that scientists do (see below) but apply mostly to experimental sciences (e.g., physics, chemistry, and biology). The elements above are often taught in the educational system
Education
Education in its broadest, general sense is the means through which the aims and habits of a group of people lives on from one generation to the next. Generally, it occurs through any experience that has a formative effect on the way one thinks, feels, or acts...

 as "the scientific method".

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 large, the vanishingly small, 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 our confidence in Newton's work.

A linearized, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:
  1. Define a question
  2. Gather information and resources (observe)
  3. Form an explanatory hypothesis
  4. Test the hypothesis by performing an experiment and collecting data in a reproducible
    Reproducibility
    Reproducibility is the ability of an experiment or study to be accurately reproduced, or replicated, by someone else working independently...

     manner
  5. Analyze the data
  6. Interpret the data and draw conclusions that serve as a starting point for new hypothesis
  7. Publish results
  8. Retest (frequently done by other scientists)


The iterative cycle inherent in this step-by-step methodology goes from point 3 to 6 back to 3 again.

While this schema outlines a typical hypothesis/testing method, it should also be noted that a number of philosophers, historians and sociologists of science (perhaps most notably Paul Feyerabend
Paul Feyerabend
Paul Karl Feyerabend was an Austrian-born philosopher of science best known for his work as a professor of philosophy at the University of California, Berkeley, where he worked for three decades . He lived a peripatetic life, living at various times in England, the United States, New Zealand,...

) claim that such descriptions of scientific method have little relation to the ways science is actually practiced.

The "operational" paradigm combines the concepts of operational definition
Operational definition
An operational definition defines something in terms of the specific process or set of validation tests used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman and is a part of...

, instrumentalism
Instrumentalism
In the philosophy of science, instrumentalism is the view that a scientific theory is a useful instrument in understanding the world. A concept or theory should be evaluated by how effectively it explains and predicts phenomena, as opposed to how accurately it describes objective...

, and utility
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....

:

The essential elements of a scientific method are operations
Operation (mathematics)
The general operation as explained on this page should not be confused with the more specific operators on vector spaces. For a notion in elementary mathematics, see arithmetic operation....

, observation
Observation
Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...

s, models, and a utility function for evaluating models.
  • Operation
    Operation (mathematics)
    The general operation as explained on this page should not be confused with the more specific operators on vector spaces. For a notion in elementary mathematics, see arithmetic operation....

     - Some action done to the system being investigated
  • Observation
    Observation
    Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...

     - What happens when the operation is done to the system
  • Model - A fact
    Fact
    A fact is something that has really occurred or is actually the case. The usual test for a statement of fact is verifiability, that is whether it can be shown to correspond to experience. Standard reference works are often used to check facts...

    , hypothesis
    Hypothesis
    A hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

    , theory
    Theory
    The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...

    , or the phenomenon itself at a certain moment
  • Utility Function - A measure of the usefulness of the model to explain, predict, and control, and of the cost of use of it. One of the elements of any scientific utility function is the refutability of the model. Another is its simplicity
    Simplicity
    Simplicity is the state or quality of being simple. It usually relates to the burden which a thing puts on someone trying to explain or understand it. Something which is easy to understand or explain is simple, in contrast to something complicated...

    , on the Principle of Parsimony more commonly known as Occam's Razor
    Occam's razor
    Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...

    .

Characterizations


Scientific method depends upon increasingly sophisticated characterizations of the subjects of investigation. (The subjects can also be called unsolved problems or the unknowns.) For example, Benjamin Franklin
Benjamin Franklin
Dr. Benjamin Franklin was one of the Founding Fathers of the United States. A noted polymath, Franklin was a leading author, printer, political theorist, politician, postmaster, scientist, musician, inventor, satirist, civic activist, statesman, and diplomat...

 conjectured, correctly, that St. Elmo's fire
St. Elmo's fire
St. Elmo's fire is a weather phenomenon in which luminous plasma is created by a coronal discharge from a grounded object in an electric field in the atmosphere St. Elmo's fire is named after St. Erasmus of Formiae St. Elmo's fire (also St. Elmo's light) is a weather phenomenon in which luminous...

 was electrical in nature
Nature
Nature, in the broadest sense, is equivalent to the natural world, physical world, or material world. "Nature" refers to the phenomena of the physical world, and also to life in general...

, 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.

The systematic, careful collection of measurements or counts of relevant quantities is often the critical difference between pseudo-sciences
Pseudoscience
Pseudoscience is a claim, belief, or practice which is presented as scientific, but which does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status...

, such as alchemy, and science, such as chemistry or biology. Scientific measurements are usually tabulated, graphed, or mapped, and statistical manipulations, such as correlation
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....

 and regression
Regression analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...

, 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 instrument
Scientific instrument
A scientific instrument can be any type of equipment, machine, apparatus or device as is specifically designed, constructed and often, through trial and error, ingeniously refined to apply utmost efficiency in the utilization of well proven physical principle, relationship or technology to...

s such as thermometers, spectroscopes, particle accelerators, or voltmeters, and the progress of a scientific field is usually intimately tied to their invention and improvement.

Uncertainty


Measurements in scientific work are also usually accompanied by estimates of their uncertainty
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...

. 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.

Definition


Measurements demand the use of operational definition
Operational definition
An operational definition defines something in terms of the specific process or set of validation tests used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman and is a part of...

s
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, electrical 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.

The scientific definition of a term sometimes differs substantially from its natural language
Natural language
In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...

 usage. For example, mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 and weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...

 overlap in meaning in common discourse, but have distinct meanings in mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

. Scientific quantities are often characterized by their units of measure
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

 which can later be described in terms of conventional physical units when communicating the work.

New theories are sometimes developed after realizing certain terms have not previously been sufficiently clearly defined. For example, Albert Einstein's
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 first paper on relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

 begins by defining simultaneity
Relativity of simultaneity
In physics, the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur...

 and the means for determining length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

. These ideas were skipped over by Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 with, "I do not define time, space, place and motion
Motion (physics)
In physics, motion is a change in position of an object with respect to time. Change in action is the result of an unbalanced force. Motion is typically described in terms of velocity, acceleration, displacement and time . An object's velocity cannot change unless it is acted upon by a force, as...

, 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
Francis Crick
Francis Harry Compton Crick OM FRS was an English molecular biologist, biophysicist, and neuroscientist, and most noted for being one of two co-discoverers of the structure of the DNA molecule in 1953, together with James D. Watson...

 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
Consciousness
Consciousness is a term that refers to the relationship between the mind and the world with which it interacts. It has been defined as: subjectivity, awareness, the ability to experience or to feel, wakefulness, having a sense of selfhood, and the executive control system of the mind...

, he actually found it easier to study awareness
Awareness
Awareness is the state or ability to perceive, to feel, or to be conscious of events, objects or sensory patterns. In this level of consciousness, sense data can be confirmed by an observer without necessarily implying understanding. More broadly, it is the state or quality of being aware of...

 in the visual system
Visual system
The visual system is the part of the central nervous system which enables organisms to process visual detail, as well as enabling several non-image forming photoresponse functions. It interprets information from visible light to build a representation of the surrounding world...

, rather than to study free will
Free will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...

, 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.

DNA-characterizations


The history of the discovery of the structure of DNA is a classic example of the elements of scientific method: in 1950 it was known that genetic inheritance had a mathematical description, starting with the studies of Gregor Mendel
Gregor Mendel
Gregor Johann Mendel was an Austrian scientist and Augustinian friar who gained posthumous fame as the founder of the new science of genetics. Mendel demonstrated that the inheritance of certain traits in pea plants follows particular patterns, now referred to as the laws of Mendelian inheritance...

, 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
William Lawrence Bragg
Sir William Lawrence Bragg CH OBE MC FRS was an Australian-born British physicist and X-ray crystallographer, discoverer of the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure. He was joint winner of the Nobel Prize for Physics in 1915. He was knighted...

 laboratory at Cambridge University
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...

 made X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

 diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

 pictures of various molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s, starting with crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

s of salt
Salt
In chemistry, salts are ionic compounds that result from the neutralization reaction of an acid and a base. They are composed of cations and anions so that the product is electrically neutral...

, 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

Another example: precession of Mercury


The characterization element can require extended and extensive study, even centuries. It took thousands of years of measurements, from the Chaldea
Chaldea
Chaldea or Chaldaea , from Greek , Chaldaia; Akkadian ; Hebrew כשדים, Kaśdim; Aramaic: ܟܐܠܕܘ, Kaldo) was a marshy land located in modern-day southern Iraq which came to briefly rule Babylon...

n, India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...

n, Persian, Greek
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....

, Arab
Arab
Arab people, also known as Arabs , are a panethnicity primarily living in the Arab world, which is located in Western Asia and North Africa. They are identified as such on one or more of genealogical, linguistic, or cultural grounds, with tribal affiliations, and intra-tribal relationships playing...

ic and European
European ethnic groups
The ethnic groups in Europe are the various ethnic groups that reside in the nations of Europe. European ethnology is the field of anthropology focusing on Europe....

 astronomers, to fully record the motion of planet Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

. Newton was able to include those measurements into consequences of his laws of motion
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...

. But the perihelion of the planet Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

's orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

 exhibits a precession that cannot be fully explained by Newton's laws of motion (see diagram to the right), though it took quite some time to realize this. The observed difference for Mercury's precession
Apsidal precession
In celestial mechanics, perihelion precession, apsidal precession or orbital precession is the precession of the orbit of a celestial body. More precisely it is the gradual rotation of the line joining the apsides of an orbit, which are the points of closest and farthest approach...

 between Newtonian theory and observation was one of the things that occurred to Einstein as a possible early test of his theory of General Relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. His relativistic calculations matched observation much more closely than did Newtonian theory (the difference is approximately 43 arc-seconds per century), .

Hypothesis development


A hypothesis
Hypothesis
A hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

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

Normally hypotheses have the form of a mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...

. Sometimes, but not always, they can also be formulated as existential statements
Existential quantification
In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ , which is called the existential quantifier...

, stating that some particular instance of the phenomenon being studied has some characteristic and causal explanations, which have the general form of universal statements
Universal quantification
In predicate logic, universal quantification formalizes the notion that something is true for everything, or every relevant thing....

, stating that every instance of the phenomenon has a particular characteristic.

Scientists are free to use whatever resources they have — their own creativity, ideas from other fields, induction
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

, Bayesian inference
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...

, and so on — to imagine possible explanations for a phenomenon under study. Charles Sanders Peirce, borrowing a page from Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 (Prior Analytics
Prior Analytics
The Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....

, 2.25) described the incipient stages of inquiry
Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.-Deduction:...

, 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
Michael Polanyi
Michael Polanyi, FRS was a Hungarian–British polymath, who made important theoretical contributions to physical chemistry, economics, and the theory of knowledge...

 made such creativity the centerpiece of his discussion of methodology.

William Glen
William Glen (geologist and historian)
William Glen, Ph.D. is a geologist and historian of science. He is the former Editor-at-Large at Stanford University Press, former Visiting Scientist/Historian at the U.S. Geological Survey, Menlo Park, and is currently Visiting Scholar at Stanford University, CA.-Books:*William Glen, 1970,...

 observes that
the success of a hypothesis, or its service to science, lies not simply in its perceived "truth", or power to displace, subsume or reduce a predecessor idea, but perhaps more in its ability to stimulate the research that will illuminate … bald suppositions and areas of vagueness.


In general scientists tend to look for theories that are "elegant
Elegance
Elegance is a synonym for beauty that has come to acquire the additional connotations of unusual effectiveness and simplicity. It is frequently used as a standard of tastefulness particularly in the areas of visual design, decoration, the sciences, and the esthetics of mathematics...

" or "beautiful
Beauty
Beauty is a characteristic of a person, animal, place, object, or idea that provides a perceptual experience of pleasure, meaning, or satisfaction. Beauty is studied as part of aesthetics, sociology, social psychology, and culture...

". In contrast to the usual English use of these terms, they here refer to a theory in accordance with the known facts, which is nevertheless relatively simple and easy to handle. Occam's Razor
Occam's razor
Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...

 serves as a rule of thumb for choosing the most desirable amongst a group of equally explanatory hypotheses.

DNA-hypotheses


Linus Pauling
Linus Pauling
Linus Carl Pauling was an American chemist, biochemist, peace activist, author, and educator. He was one of the most influential chemists in history and ranks among the most important scientists of the 20th century...

 proposed that DNA might be a triple helix. This hypothesis was also considered by Francis Crick
Francis Crick
Francis Harry Compton Crick OM FRS was an English molecular biologist, biophysicist, and neuroscientist, and most noted for being one of two co-discoverers of the structure of the DNA molecule in 1953, together with James D. Watson...

 and James D. Watson
James D. Watson
James Dewey Watson is an American molecular biologist, geneticist, and zoologist, best known as one of the co-discoverers of the structure of DNA in 1953 with Francis Crick...

 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—see section on "DNA-predictions" below)

Predictions from the hypothesis


Any useful hypothesis will enable prediction
Prediction
A prediction or forecast is a statement about the way things will happen in the future, often but not always based on experience or knowledge...

s, by reasoning including deductive reasoning
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

. 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.

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

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. Thus, much scientifically based speculation might convince one (or many) that the hypothesis that other intelligent species exist is true, but there being not experiment now known which can test this hypothesis, science itself can have little to say about the possibility. In future, some new technique might lead to an experimental test and the speculation become part of accepted science.

DNA-predictions


James D. Watson
James D. Watson
James Dewey Watson is an American molecular biologist, geneticist, and zoologist, best known as one of the co-discoverers of the structure of DNA in 1953 with Francis Crick...

, Francis Crick
Francis Crick
Francis Harry Compton Crick OM FRS was an English molecular biologist, biophysicist, and neuroscientist, and most noted for being one of two co-discoverers of the structure of the DNA molecule in 1953, together with James D. Watson...

, 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.

In their first paper, Watson and Crick also noted that the double helix structure they proposed provided a simple mechanism for DNA replication
DNA replication
DNA replication is a biological process that occurs in all living organisms and copies their DNA; it is the basis for biological inheritance. The process starts with one double-stranded DNA molecule and produces two identical copies of the molecule...

, 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

Another example: general relativity


Einstein's theory of General Relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

 makes several specific predictions about the observable structure of space-time, such as that light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 bends in a gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

, 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
Solar eclipse
As seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...

 supported General Relativity rather than Newtonian gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

.

Experiments


Once predictions are made, they can be sought by experiments. If test results contradict the predictions, the hypotheses which made them are called into question and become less tenable. Sometimes experiments are conducted incorrectly and are not very useful. If the 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) under differing conditions to see what varies or what remains the same. We vary the conditions for each measurement, to help isolate what has changed. Mill's canons can then help us figure out what the important factor is. Factor analysis
Factor analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...

 is one technique for discovering the important factor in an effect.

Depending on the predictions, the experiments can have different shapes. It could be a classical experiment in a laboratory setting, a double-blind
Double-blind
A blind or blinded experiment is a scientific experiment where some of the people involved are prevented from knowing certain information that might lead to conscious or subconscious bias on their part, invalidating the results....

 study or an archaeological excavation. Even taking a plane from New York
New York
New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...

 to Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...

 is an experiment which tests the aerodynamical
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

 hypotheses used for constructing the plane.

Scientists assume an attitude of openness and accountability on the part of those conducting an experiment. 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
Hipparchus
Hipparchus, the common Latinization of the Greek Hipparkhos, can mean:* Hipparchus, the ancient Greek astronomer** Hipparchic cycle, an astronomical cycle he created** Hipparchus , a lunar crater named in his honour...

 (190-120 BCE), when determining a value for the precession of the Earth, while controlled experiments
Scientific control
Scientific control allows for comparisons of concepts. It is a part of the scientific method. Scientific control is often used in discussion of natural experiments. For instance, during drug testing, scientists will try to control two groups to keep them as identical and normal as possible, then...

 can be seen in the works of Jābir ibn Hayyān (721-815 CE), al-Battani (853–929) and Alhazen (965-1039).

DNA-experiments


Watson and Crick showed an initial (and incorrect) proposal for the structure of DNA to a team from Kings College - Rosalind Franklin
Rosalind Franklin
Rosalind Elsie Franklin was a British biophysicist and X-ray crystallographer who made critical contributions to the understanding of the fine molecular structures of DNA, RNA, viruses, coal and graphite...

, Maurice Wilkins
Maurice Wilkins
Maurice Hugh Frederick Wilkins CBE FRS was a New Zealand-born English physicist and molecular biologist, and Nobel Laureate whose research contributed to the scientific understanding of phosphorescence, isotope separation, optical microscopy and X-ray diffraction, and to the development of radar...

, and Raymond Gosling
Raymond Gosling
Raymond Gosling is a distinguished scientist who worked with both Maurice Wilkins and Rosalind Franklin at King's College London in deducing the structure of DNA, under the direction of Sir John Randall. His other KCL colleagues included Alex Stokes and Herbert Wilson.-Early years:He was born in...

. Franklin immediately spotted the flaws which concerned the water content. Later Watson saw Franklin's detailed X-ray diffraction images
Photo 51
Photo 51 is the nickname given to an X-ray diffraction image of DNA taken by Rosalind Franklin in 1952 that was critical evidence in identifying the structure of DNA. The photo was taken by Franklin while working at King's College London in Sir John Randall's group.James D...

 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

Evaluation and improvement


The scientific process is iterative. At any stage it is possible to refine its accuracy and precision
Accuracy and precision
In the fields of science, engineering, industry and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's actual value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which...

, 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.

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.

DNA-iterations


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
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...

 by concrete modeling of the physical shapes of the nucleotide
Nucleotide
Nucleotides are molecules that, when joined together, make up the structural units of RNA and DNA. In addition, nucleotides participate in cellular signaling , and are incorporated into important cofactors of enzymatic reactions...

s which comprise it. They were guided by the bond lengths which had been deduced by Linus Pauling
Linus Pauling
Linus Carl Pauling was an American chemist, biochemist, peace activist, author, and educator. He was one of the most influential chemists in history and ranks among the most important scientists of the 20th century...

 and by Rosalind Franklin
Rosalind Franklin
Rosalind Elsie Franklin was a British biophysicist and X-ray crystallographer who made critical contributions to the understanding of the fine molecular structures of DNA, RNA, viruses, coal and graphite...

's X-ray diffraction images. ..DNA Example

Confirmation


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
Georg Wilhelm Richmann
Georg Wilhelm Richmann was a German physicist who lived in Russia....

 was killed by ball lightning
Ball lightning
Ball lightning is an unexplained atmospheric electrical phenomenon. The term refers to reports of luminous, usually spherical objects which vary from pea-sized to several metres in diameter. It is usually associated with thunderstorms, but lasts considerably longer than the split-second flash of a...

 (1753) when attempting to replicate the 1752 kite-flying experiment of Benjamin Franklin
Benjamin Franklin
Dr. Benjamin Franklin was one of the Founding Fathers of the United States. A noted polymath, Franklin was a leading author, printer, political theorist, politician, postmaster, scientist, musician, inventor, satirist, civic activist, statesman, and diplomat...

.

To protect against bad science and fraudulent data, government research-granting agencies such as the National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...

, and science journals including Nature and Science, have a policy that researchers must archive their data and methods so other researchers can test the data and methods and build on the research that has gone before. Scientific data archiving
Scientific data archiving
Scientific data archiving refers to the long-term storage of scientific data and methods. The various scientific journals have differing policies regarding how much of their data and methods scientists are required to store in a public archive, and what is actually archived varies widely between...

 can be done at a number of national archives in the U.S. or in the World Data Center
World Data Center
The World Data Center system was created to archive and distribute data collected from the observational programs of the 1957-1958 International Geophysical Year. Originally established in the United States, Europe, Soviet Union, and Japan, the WDC system has since expanded to other countries and...

.

Classical model


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
Abductive reasoning
Abduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...

, deductive
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

, and inductive
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

 inference, and also treated the compound forms such as reasoning by analogy
Analogy
Analogy is a cognitive process of transferring information or meaning from a particular subject to another particular subject , and a linguistic expression corresponding to such a process...

.

Pragmatic model



In 1877, Charles Sanders Peirce (icon like "purse"; 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, 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:
  1. The method of tenacity (policy of sticking to initial belief) — which brings comforts and decisiveness but leads to trying to ignore contrary information and others' views as if truth were intrinsically private, not public. It goes against the social impulse and easily falters since one may well notice when another's opinion is as good as one's own initial opinion. Its successes can shine but tend to be transitory.
  2. The method of authority — which overcomes disagreements but sometimes brutally. Its successes can be majestic and long-lived, but it cannot operate thoroughly enough to suppress doubts indefinitely, especially when people learn of other societies present and past.
  3. The method of congruity or the a priori or the dilettante or "what is agreeable to reason" — which promotes conformity less brutally but depends on taste and fashion in paradigm
    Paradigm
    The word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...

    s and can go in circles over time, along with barren disputation. It is more intellectual and respectable but, like the first two methods, sustains accidental and capricious beliefs, destining some minds to doubts.
  4. The scientific method — the method wherein inquiry regards itself as fallible
    Fallibilism
    Fallibilism is the philosophical principle that human beings could be wrong about their beliefs, expectations, or their understanding of the world...

     and purposely tests itself and criticizes, corrects, and improves itself.


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 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.

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 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.

Paying special attention to the generation of explanations, Peirce outlined scientific method as a 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):

1. Abduction
Abductive reasoning
Abduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...

(or retroduction). Guessing, inference to explanatory hypotheses for selection of those best worth trying. From abduction, Peirce distinguishes induction as inferring, on the basis of tests, the proportion of truth in the hypothesis. Every inquiry, whether into ideas, brute facts, or norms and laws, arises from surprising observations in one or more of those realms (and for example at any stage of an inquiry already underway). All explanatory content of theories comes from abduction, which guesses a new or outside idea so as to account in a simple, economical way for a surprising or complicative phenomenon. Oftenest, even a well-prepared mind guesses wrong. But the modicum of success of our guesses far exceeds that of sheer luck and seems born of attunement to nature by instincts developed or inherent, especially insofar as best guesses are optimally plausible and simple in the sense, said Peirce, of the "facile and natural", as by Galileo's natural light of reason and as distinct from "logical simplicity". Abduction is the most fertile but least secure mode of inference. Its general rationale is inductive: it succeeds often enough and, without it, there is no hope of sufficiently expediting inquiry (often multi-generational) toward new truths. Coordinative method leads from abducing a plausible hypothesis to judging it for its testability and for how its trial would economize inquiry itself. Peirce calls his pragmatism
Pragmaticism
Pragmaticism is a term used by Charles Sanders Peirce for his pragmatic philosophy starting in 1905, in order to distance himself and it from pragmatism, the original name, which had been used in a manner he did not approve of in the "literary journals"...

 "the logic of abduction". His pragmatic maxim
Pragmatic maxim
The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce...

 is: "Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object". His pragmatism is a method of reducing conceptual confusions fruitfully by equating the meaning of any conception with the conceivable practical implications of its object's conceived effects — a method of experimentational mental reflection hospitable to forming hypotheses and conducive to testing them. It favors efficiency. The hypothesis, being insecure, needs to have practical implications leading at least to mental tests and, in science, lending themselves to scientific tests. A simple but unlikely guess, if uncostly to test for falsity, may belong first in line for testing. A guess is intrinsically worth testing if it has instinctive plausibility or reasoned objective probability, while subjective likelihood, though reasoned, can be misleadingly seductive. Guesses can be chosen for trial strategically, for their caution (for which Peirce gave as example the game of Twenty Questions
Twenty Questions
Twenty Questions is a spoken parlor game which encourages deductive reasoning and creativity. It originated in the United States and escalated in popularity during the late 1940s when it became the format for a successful weekly radio quiz program....

), breadth, and incomplexity. One can hope to discover only that which time would reveal through a learner's sufficient experience anyway, so the point is to expedite it; the economy of research is what demands the "leap" of abduction and governs its art.

2. Deduction
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

. Two stages:
i. Explication. Unclearly premissed, but deductive, analysis of the hypothesis in order to render its parts as clear as possible.
ii. Demonstration: Deductive Argumentation, Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

ean in procedure. Explicit deduction of hypothesis's consequences as predictions, for induction to test, about evidence to be found. Corollarial
Corollary
A corollary is a statement that follows readily from a previous statement.In mathematics a corollary typically follows a theorem. The use of the term corollary, rather than proposition or theorem, is intrinsically subjective...

 or, if needed, Theorematic.


3. Induction
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

. The long-run validity of the rule of induction is deducible from the principle (presuppositional to reasoning in general) that the real is only the object of the final opinion to which adequate investigation would lead; anything to which no such process would ever lead would not be real. Induction involving ongoing tests or observations follows a method which, sufficiently persisted in, will diminish its error below any predesignate degree. Three stages:
i. Classification. Unclearly premissed, but inductive, classing of objects of experience under general ideas.
ii. Probation: direct (and explicit) Inductive Argumentation. Crude (the enumeration of instances) or Gradual (new estimate of proportion of truth in the hypothesis after each test). Gradual Induction is Qualitative or Quantitative; if Qualitative, then dependent on weighting
Weighting
The process of weighting involves emphasizing the contribution of some aspects of a phenomenon to a final effect or result — giving them 'more weight' in the analysis. That is, rather than each variable in the data contributing equally to the final result, some data are adjusted to contribute...

s of qualities or characters; if Quantitative, then dependent on measurements, or on statistics, or on countings.
iii. Sentential Induction. "...which, by Inductive reasonings, appraises the different Probations singly, then their combinations, then makes self-appraisal of these very appraisals themselves, and passes final judgment on the whole result".

Computational approaches


Many subspecialties of applied logic and computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

, such as artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...

, machine learning
Machine learning
Machine learning, a branch of artificial intelligence, is a scientific discipline concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases...

, computational learning theory
Computational learning theory
In theoretical computer science, computational learning theory is a mathematical field related to the analysis of machine learning algorithms.-Overview:Theoretical results in machine learning mainly deal with a type of...

, inferential statistics, and knowledge representation
Knowledge representation
Knowledge representation is an area of artificial intelligence research aimed at representing knowledge in symbols to facilitate inferencing from those knowledge elements, creating new elements of knowledge...

, are concerned with setting out computational, logical, and statistical frameworks for the various types of inference involved in scientific inquiry. In particular, they contribute hypothesis formation
Abductive reasoning
Abduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...

, logical deduction
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

, and empirical testing
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

. Some of these applications draw on measures
Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, and volume...

 of complexity
Complexity
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

 from algorithmic information theory
Algorithmic information theory
Algorithmic information theory is a subfield of information theory and computer science that concerns itself with the relationship between computation and information...

 to guide the making of predictions from prior distributions
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

 of experience, for example, see the complexity measure called the speed prior
Speed prior
Jürgen Schmidhuber's speed prior is a complexity measure similar to Kolmogorov complexity, except that it is based on computation speed as well as programlength.The speed prior complexity of a program is its...

from which a computable strategy for optimal inductive reasoning can be derived.

Communication and community


Frequently a 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 one of the defining elements of a scientific community
Scientific community
The scientific community consists of the total body of scientists, its relationships and interactions. It is normally divided into "sub-communities" each working on a particular field within science. Objectivity is expected to be achieved by the scientific method...

. Various techniques have been developed to ensure the integrity of that scientific method within such an environment.

Peer review evaluation


Scientific journals use a process of peer review
Peer review
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...

, in which scientists' manuscripts are submitted by editors of scientific journals to (usually one to three) fellow (usually anonymous) scientists familiar with the field for evaluation. The referees may or may not recommend publication, publication with suggested modifications, or, sometimes, publication in another journal. This serves to keep the scientific literature free of unscientific or pseudoscientific
Pseudoscience
Pseudoscience is a claim, belief, or practice which is presented as scientific, but which does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status...

 work, to help cut down on obvious errors, and generally otherwise to improve the quality of the material. The peer review process can have limitations when considering research outside the conventional scientific paradigm: problems of "groupthink
Groupthink
Groupthink is a psychological phenomenon that occurs within groups of people. It is the mode of thinking that happens when the desire for harmony in a decision-making group overrides a realistic appraisal of alternatives. Group members try to minimize conflict and reach a consensus decision without...

" can interfere with open and fair deliberation of some new research.

Documentation and replication



Sometimes experimenters may make systematic errors during their experiments, unconsciously veer from a scientific method (Pathological science
Pathological science
Pathological science is the process in science in which "people are tricked into false results ... by subjective effects, wishful thinking or threshold interactions". The term was first used by Irving Langmuir, Nobel Prize-winning chemist, during a 1953 colloquium at the Knolls Research Laboratory...

) for various reasons, or, in rare cases, deliberately report false results. Consequently, it is a common practice for other scientists to attempt to repeat the experiments in order to duplicate the results, thus further validating the hypothesis.

Archiving


As a result, researchers are expected to practice scientific data archiving
Scientific data archiving
Scientific data archiving refers to the long-term storage of scientific data and methods. The various scientific journals have differing policies regarding how much of their data and methods scientists are required to store in a public archive, and what is actually archived varies widely between...

 in compliance with the policies of government funding agencies and scientific journals. Detailed records of their experimental procedures, raw data, statistical analyses and source code are preserved in order to provide evidence of the effectiveness and integrity of the procedure and assist in reproduction
Reproducibility
Reproducibility is the ability of an experiment or study to be accurately reproduced, or replicated, by someone else working independently...

. 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.

Data sharing


When additional information is needed before a study can be reproduced, the author of the study is expected to provide it promptly. If the author refuses to share data
Data sharing
Data sharing is the practice of making data used for scholarly research available to other investigators. Replication has a long history in science...

, appeals can be made to the journal editors who published the study or to the institution which funded the research.

Limitations


Since it is impossible for a scientist to 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 in order to select and report the experimental conditions. The observations are hence sometimes described as being 'theory-laden'.

Dimensions of practice


The primary constraints on contemporary western science are:
  • Publication, i.e. Peer review
    Peer review
    Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...

  • Resources (mostly funding)

It has not always been like this: in the old days of the "gentleman scientist
Gentleman scientist
A gentleman scientist is a financially independent scientist who pursues scientific study as a hobby. The term arose in post-Renaissance Europe but became less common in the 20th century as government and private funding increased.-History:...

" funding (and to a lesser extent publication) were far weaker constraints.

Both of these constraints indirectly bring in a scientific method — work that too obviously violates the constraints will be difficult to publish and difficult to get funded. Journals do not require submitted papers to conform to anything more specific than "good scientific practice" and this is mostly enforced by peer review. Originality, importance and interest are more important - see for example the author guidelines for Nature
Nature (journal)
Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...

.

Philosophy and sociology of science


Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science
Demarcation problem
The demarcation problem in the philosophy of science is about how and where to draw the lines around science. The boundaries are commonly drawn between science and non-science, between science and pseudoscience, between science and philosophy and between science and religion...

, and the ethic
Research ethics
Research ethics involves the application of fundamental ethical principles to a variety of topics involving scientific research. These include the design and implementation of research involving human experimentation, animal experimentation, various aspects of academic scandal, including scientific...

 that is implicit in science. There are basic assumptions derived from philosophy 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
Naturalism (philosophy)
Naturalism commonly refers to the philosophical viewpoint that the natural universe and its natural laws and forces operate in the universe, and that nothing exists beyond the natural universe or, if it does, it does not affect the natural universe that we know...

 form the basis on which science is grounded. Logical Positivist
Logical positivism
Logical positivism is a philosophy that combines empiricism—the idea that observational evidence is indispensable for knowledge—with a version of rationalism incorporating mathematical and logico-linguistic constructs and deductions of epistemology.It may be considered as a type of analytic...

, empiricist
Empiricism
Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...

, falsificationist
Falsifiability
Falsifiability or refutability of an assertion, hypothesis or theory is the logical possibility that it can be contradicted by an observation or the outcome of a physical experiment...

, and other theories have claimed to give a definitive account of the logic of science, but each has in turn been criticized.

Thomas Kuhn
Thomas Kuhn
Thomas Samuel Kuhn was an American historian and philosopher of science whose controversial 1962 book The Structure of Scientific Revolutions was deeply influential in both academic and popular circles, introducing the term "paradigm shift," which has since become an English-language staple.Kuhn...

 examined the history of science in his The Structure of Scientific Revolutions
The Structure of Scientific Revolutions
The Structure of Scientific Revolutions , by Thomas Kuhn, is an analysis of the history of science. Its publication was a landmark event in the history, philosophy, and sociology of scientific knowledge and it triggered an ongoing worldwide assessment and reaction in — and beyond — those scholarly...

, 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.

Norwood Russell Hanson
Norwood Russell Hanson
Norwood Russell Hanson was a philosopher of science. Hanson was a pioneer in advancing the argument that observation is theory-laden – that observation language and theory language are deeply interwoven – and that historical and contemporary comprehension are similarly deeply interwoven...

, Imre Lakatos
Imre Lakatos
Imre Lakatos was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his...

 and Thomas Kuhn
Thomas Kuhn
Thomas Samuel Kuhn was an American historian and philosopher of science whose controversial 1962 book The Structure of Scientific Revolutions was deeply influential in both academic and popular circles, introducing the term "paradigm shift," which has since become an English-language staple.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
Gestalt
Die Gestalt is a German word for form or shape. It is used in English to refer to a concept of 'wholeness'. Gestalt may also refer to:* Gestalt psychology , a theory of mind and brain, describing the Gestalt effect....

 to show how preconceptions can affect both observation and description. He opens Chapter 1 with a discussion of the Golgi bodies
Golgi apparatus
The Golgi apparatus is an organelle found in most eukaryotic cells. It was identified in 1898 by the Italian physician Camillo Golgi, after whom the Golgi apparatus is named....

 and their initial rejection as an artefact of staining technique, and a discussion of Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

 and Kepler
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...

 observing the dawn and seeing a "different" sun rise despite the same physiological phenomenon. Kuhn and Feyerabend acknowledge the pioneering significance of his work.

Kuhn (1961) said the scientist generally has a theory in mind before designing and undertaking experiments so as to make empirical observations, and that the "route from theory to measurement can almost never be traveled backward". This implies that the way in which theory is tested is dictated by the nature of the theory itself, which led Kuhn (1961, p. 166) 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".

Paul Feyerabend
Paul Feyerabend
Paul Karl Feyerabend was an Austrian-born philosopher of science best known for his work as a professor of philosophy at the University of California, Berkeley, where he worked for three decades . He lived a peripatetic life, living at various times in England, the United States, New Zealand,...

 similarly examined the history of science, and was led to deny that science is genuinely a methodological process. In his book Against Method
Against Method
Against Method is a book by Paul Feyerabend. In this work, Feyerabend argues that science is an anarchic enterprise. In the context of this work, the term anarchy refers to epistemological anarchy...

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 a scientific method wish to express a single universally valid rule, Feyerabend jokingly suggests, it should be 'anything goes'. Criticisms such as his led to the strong programme
Strong programme
The strong programme or Strong Sociology is a variety of the sociology of scientific knowledge particularly associated with David Bloor, Barry Barnes, Harry Collins, Donald A. MacKenzie, and John Henry. The strong programme's influence on Science and Technology Studies is credited as being...

, a radical approach to the sociology of science.

In his 1958 book, Personal Knowledge, chemist and philosopher Michael Polanyi
Michael Polanyi
Michael Polanyi, FRS was a Hungarian–British polymath, who made important theoretical contributions to physical chemistry, economics, and the theory of knowledge...

 (1891–1976) criticized the common view that the scientific method is purely objective and generates objective knowledge. Polanyi cast this view as a misunderstanding of the scientific method and of the nature of scientific inquiry, generally. He argued that scientists do and must follow personal passions in appraising facts and in determining which scientific questions to investigate. He concluded that a structure of liberty is essential for the advancement of science - that the freedom to pursue science for its own sake is a prerequisite for the production of knowledge through peer review and the scientific method.

The postmodernist
Postmodernism
Postmodernism is a philosophical movement evolved in reaction to modernism, the tendency in contemporary culture to accept only objective truth and to be inherently suspicious towards a global cultural narrative or meta-narrative. Postmodernist thought is an intentional departure from the...

 critiques of science have themselves been the subject of intense controversy. This ongoing debate, known as the science wars
Science wars
The science wars were a series of intellectual exchanges, between scientific realists and postmodernist critics, about the nature of scientific theory which took place principally in the US in the 1990s...

, is the result of conflicting values and assumptions between the postmodernist and realist
Scientific realism
Scientific realism is, at the most general level, the view that the world described by science is the real world, as it is, independent of what we might take it to be...

 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
Scientific realism
Scientific realism is, at the most general level, the view that the world described by science is the real world, as it is, independent of what we might take it to be...

 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.

Luck and science


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
Louis Pasteur
Louis Pasteur was a French chemist and microbiologist born in Dole. He is remembered for his remarkable breakthroughs in the causes and preventions of diseases. His discoveries reduced mortality from puerperal fever, and he created the first vaccine for rabies and anthrax. His experiments...

 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 professor of economics 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.

Psychologist Kevin Dunbar says the process of discovery often starts with researchers finding bugs in their experiments. These unexpected results lead researchers to try and fix what they think is an error in their methodology. 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.

History


The development of the scientific method is inseparable from the history of science
History of science
The history of science is the study of the historical development of human understandings of the natural world and the domains of the social sciences....

 itself. Ancient Egypt
Ancient Egypt
Ancient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...

ian documents describe empirical methods in astronomy
History of astronomy
Astronomy is the oldest of the natural sciences, dating back to antiquity, with its origins in the religious, mythological, and astrological practices of pre-history: vestiges of these are still found in astrology, a discipline long interwoven with public and governmental astronomy, and not...

, mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....

, and medicine. The ancient Greek philosopher Thales
Thales
Thales of Miletus was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece. Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition...

 in the 6th century BC refused to accept supernatural, religious or mythological explanations for natural phenomena, proclaiming that every event had a natural cause. The development of deductive reasoning
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

 by Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

 was an important step towards the scientific method. Empiricism
Empiricism
Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...

 seems to have been formalized by Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

, who believed that universal truths could be reached via induction
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

.

There are hints of experimental methods from the Classical world (e.g., those reported by Archimedes in a report recovered early in the 20th century CE from an overwritten manuscript
Archimedes Palimpsest
The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex. It originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors, which was overwritten with a religious text.Archimedes lived in the...

), but the first clear instances of an experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

al scientific method seem to have been developed by Islamic scientists
Islamic science
Science in the medieval Islamic world, also known as Islamic science or Arabic science, is the science developed and practised in the Islamic world during the Islamic Golden Age . During this time, Indian, Iranian and especially Greek knowledge was translated into Arabic...

 who introduced the use of experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

ation and quantification
Quantification
Quantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method.In logic,...

 within a generally empirical orientation. For example, Alhazen performed optical
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

 and physiological experiments, reported in his manifold works, the most famous being Book of Optics (1021). The modern scientific method crystallized no later than in the 17th and 18th centuries. In his work Novum Organum
Novum Organum
The Novum Organum, full original title Novum Organum Scientiarum, is a philosophical work by Francis Bacon, written in Latin and published in 1620. The title translates as new instrument, i.e. new instrument of science. This is a reference to Aristotle's work Organon, which was his treatise on...

(1620) — a reference to Aristotle's Organon
Organon
The Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...

Francis Bacon
Francis Bacon
Francis Bacon, 1st Viscount St Albans, KC was an English philosopher, statesman, scientist, lawyer, jurist, author and pioneer of the scientific method. He served both as Attorney General and Lord Chancellor of England...

 outlined a new system of logic to improve upon the old philosophical
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

 process of syllogism
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

. Then, in 1637, René Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

 established the framework for a scientific method's guiding principles in his treatise, Discourse on Method
Discourse on Method
The Discourse on the Method is a philosophical and autobiographical treatise published by René Descartes in 1637. Its full name is Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences .The Discourse on Method is best known...

. The writings of Alhazen, Bacon and Descartes are considered critical in the historical development of the modern scientific method, as are those of John Stuart Mill
John Stuart Mill
John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...

.
In the late 19th century, Charles Sanders Peirce proposed a schema that would turn out to have considerable influence in the development of current scientific method generally. Peirce accelerated the progress on several fronts. Firstly, speaking in broader context in "How to Make Our Ideas Clear" (1878), Peirce outlined an objectively verifiable method to test the truth of putative knowledge on a way that goes beyond mere foundational alternatives, focusing upon both deduction and induction. He thus placed induction and deduction in a complementary rather than competitive context (the latter of which had been the primary trend at least since David Hume
David Hume
David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...

, who wrote in the mid-to-late 18th century). Secondly, and of more direct importance to modern method, Peirce put forth the basic schema for hypothesis/testing that continues to prevail today. Extracting the theory of inquiry from its raw materials in classical logic, he refined it in parallel with the early development of symbolic logic to address the then-current problems in scientific reasoning. Peirce examined and articulated the three fundamental modes of reasoning that, as discussed above in this article, play a role in inquiry today, the processes that are currently known as abductive
Abductive reasoning
Abduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...

, deductive
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

, and inductive
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

 inference. Thirdly, he played a major role in the progress of symbolic logic itself — indeed this was his primary specialty.

Beginning in the 1930s, Karl Popper
Karl Popper
Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...

 argued that there is no such thing as inductive reasoning. All inferences ever made, including in science, are purely deductive according to this view. Accordingly, he claimed that the empirical character of science has nothing to do with induction—but with the deductive property of falsifiability
Falsifiability
Falsifiability or refutability of an assertion, hypothesis or theory is the logical possibility that it can be contradicted by an observation or the outcome of a physical experiment...

 that scientific hypotheses have. Contrasting his views with inductivism and positivism, he even denied the existence of scientific method: "(1) There is no method of discovering a scientific theory (2) There is no method for ascertaining the truth of a scientific hypothesis, i.e., no method of verification; (3) There is no method for ascertaining whether a hypothesis is 'probable', or probably true". Instead, he held that there is only one universal method, a method not particular to science: The negative method of criticism, or colloquially termed trial and error
Trial and error
Trial and error, or trial by error, is a general method of problem solving, fixing things, or for obtaining knowledge."Learning doesn't happen from failure itself but rather from analyzing the failure, making a change, and then trying again."...

. It covers not only all products of the human mind, including science, mathematics, philosophy, art and so on, but also the evolution of life. Following Peirce and others, Popper argued that science is fallible and has no authority. In contrast to empiricist-inductivist views, he welcomed metaphysics and philosophical discussion and even gave qualified support to myths and pseudosciences. Popper's view has become known as critical rationalism
Critical rationalism
Critical rationalism is an epistemological philosophy advanced by Karl Popper. Popper wrote about critical rationalism in his works, The Open Society and its Enemies Volume 2, and Conjectures and Refutations.- Criticism, not support :...

.

Relationship with mathematics


Science is the process of gathering, comparing, and evaluating proposed models against observable
Observable
In physics, particularly in quantum physics, a system observable is a property of the system state that can be determined by some sequence of physical operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value off...

s. 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 can clearly 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 proven; at such a stage, that statement would be called a conjecture
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...

. 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.

Mathematical work and scientific work can inspire each other. For example, the technical concept of time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

 arose in science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...

 has been proven using time as a mathematical concept in which objects can flow (see Ricci flow
Ricci flow
In differential geometry, the Ricci flow is an intrinsic geometric flow. It is a process that deforms the metric of a Riemannian manifold in a way formally analogous to the diffusion of heat, smoothing out irregularities in the metric....

).

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
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The Unreasonable Effectiveness of Mathematics in the Natural Sciences is the title of an article published in 1960 by the physicist Eugene Wigner...

, is a very well known account of the issue from a Nobel Prize physicist. In fact, some observers (including some well known mathematicians such as Gregory Chaitin
Gregory Chaitin
Gregory John Chaitin is an Argentine-American mathematician and computer scientist.-Mathematics and computer science:Beginning in 2009 Chaitin has worked on metabiology, a field parallel to biology dealing with the random evolution of artificial software instead of natural software .Beginning in...

, and others such as Lakoff and Núñez
Where Mathematics Comes From
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist...

) have suggested that mathematics is the result of practitioner bias and human limitation (including cultural ones), somewhat like the post-modernist view of science.

George Pólya
George Pólya
George Pólya was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory...

's work on problem solving
Problem solving
Problem solving is a mental process and is part of the larger problem process that includes problem finding and problem shaping. Consideredthe most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of...

, the construction of mathematical proofs
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...

, and heuristic
Heuristic
Heuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...

 show that the mathematical method and the scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps.
Mathematical method
How to Solve It
How to Solve It is a small volume by mathematician George Pólya describing methods of problem solving.- Four principles :How to Solve It suggests the following steps when solving a mathematical problem:...

Scientific method
1 Understanding
Understanding
Understanding is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to think about it and use concepts to deal adequately with that object....

Characterization from experience and observation
2 Analysis
Analysis
Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle , though analysis as a formal concept is a relatively recent development.The word is...

Hypothesis: a proposed explanation
3 Synthesis Deduction: prediction from the hypothesis
4 Review
Review
A review is an evaluation of a publication, a product or a service, such as a movie , video game, musical composition , book ; a piece of hardware like a car, home appliance, or computer; or an event or performance, such as a live music concert, a play, musical theater show or dance show...

/Extend
Generalization
A generalization of a concept is an extension of the concept to less-specific criteria. It is a foundational element of logic and human reasoning. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements. As such, it...

Test and experiment


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
Pappus of Alexandria
Pappus of Alexandria was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection , and for Pappus's Theorem in projective geometry...

, 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 Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

ean exposition of step-by-step details of the proof; review involves reconsidering and re-examining the result and the path taken to it.

Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...

, when asked how he came about his theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...

s, once replied "durch planmässiges Tattonieren" (through systematic palpable experimentation
Constructivism (mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption, one still has not found the object and therefore not proved its...

).

Imre Lakatos
Imre Lakatos
Imre Lakatos was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his...

 argued that mathematicians actually use contradiction, criticism and revision as principles for improving their work.

See also



  • Confirmability
  • Contingency
  • Falsifiability
    Falsifiability
    Falsifiability or refutability of an assertion, hypothesis or theory is the logical possibility that it can be contradicted by an observation or the outcome of a physical experiment...

  • Hypothesis
    Hypothesis
    A hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

  • Hypothesis testing
    Statistical hypothesis testing
    A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold...

  • Inquiry
    Inquiry
    An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.-Deduction:...

  • Information theory
    Information theory
    Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...


  • Logic
    Logic
    In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

    • Abductive reasoning
      Abductive reasoning
      Abduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...

    • Deductive reasoning
      Deductive reasoning
      Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

    • Inductive reasoning
      Inductive reasoning
      Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

    • Inference
      Inference
      Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...

    • Tautology
      Tautology (logic)
      In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...


  • Methodology
    Methodology
    Methodology is generally a guideline for solving a problem, with specificcomponents such as phases, tasks, methods, techniques and tools . It can be defined also as follows:...

    • Baconian method
      Baconian method
      The Baconian method is the investigative method developed by Sir Francis Bacon. The method was put forward in Bacon's book Novum Organum , or 'New Method', and was supposed to replace the methods put forward in Aristotle's Organon...

    • Empirical method
      Empirical method
      The empirical method is generally taken to mean the approach of using a collection of data to base a theory or derive a conclusion in science...

    • Historical method
      Historical method
      Historical method comprises the techniques and guidelines by which historians use primary sources and other evidence to research and then to write histories in the form of accounts of the past. The question of the nature, and even the possibility, of a sound historical method is raised in the...

    • Philosophical method
      Philosophical method
      Philosophical method is the study of how to do philosophy. A common view among philosophers is that philosophy is distinguished by the methods that philosophers follow in addressing philosophical questions...

    • Phronetic method
    • Scholarly method
      Scholarly method
      Scholarly method or scholarship is the body of principles and practices used by scholars to make their claims about the world as valid and trustworthy as possible, and to make them known to the scholarly public.-Methods:...

    • Strong inference
      Strong inference
      In philosophy of science, strong inference is a model of scientific inquiry that emphasises the need for alternative hypotheses, rather than a single hypothesis in order to avoid confirmation bias....

  • Mathematics
    Mathematics
    Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

  • OGHET
    OGHET
    OGHET - An acronym by which the Scientific Method can be remembered.Observe - Look for patterns in the process you are interested in. Ask questions about the underlying nature of what you perceive. Keep a journal....


  • Operationalization
    Operationalization
    In humanities, operationalization is the process of defining a fuzzy concept so as to make the concept clearly distinguishable or measurable and to understand it in terms of empirical observations...

  • Quantitative research
    Quantitative research
    In the social sciences, quantitative research refers to the systematic empirical investigation of social phenomena via statistical, mathematical or computational techniques. The objective of quantitative research is to develop and employ mathematical models, theories and/or hypotheses pertaining to...

  • Reproducibility
    Reproducibility
    Reproducibility is the ability of an experiment or study to be accurately reproduced, or replicated, by someone else working independently...

  • Research
    Research
    Research can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...

  • Social research
    Social research
    Social research refers to research conducted by social scientists. Social research methods may be divided into two broad categories:* Quantitative designs approach social phenomena through quantifiable evidence, and often rely on statistical analysis of many cases to create valid and reliable...

  • Statistics
    Statistics
    Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

  • Testability
    Testability
    Testability, a property applying to an empirical hypothesis, involves two components: the logical property that is variously described as contingency, defeasibility, or falsifiability, which means that counterexamples to the hypothesis are logically possible, and the practical feasibility of...

  • Theory
    Theory
    The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...

  • Verification and Validation
    Verification and Validation
    In software project management, software testing, and software engineering, verification and validation is the process of checking that a software system meets specifications and that it fulfills its intended purpose...



Problems and issues



  • Induction
    Inductive reasoning
    Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

  • Problem of induction
    Problem of induction
    The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either:...

  • Occam's razor
    Occam's razor
    Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...

  • Skeptical hypotheses

  • Poverty of the stimulus
    Poverty of the stimulus
    In linguistics, the poverty of the stimulus is the assertion that natural language grammar is unlearnable given the relatively limited data available to children learning a language, and therefore that this knowledge is supplemented with some sort of innate linguistic capacity...

  • Reference class problem
    Reference class problem
    In statistics, the reference class problem is the problem of deciding what class to use when calculating the probability applicable to a particular case...

  • Underdetermination
    Underdetermination
    In scientific theory, underdetermination refers to situations where the evidence available is insufficient to identify which belief we should hold about that evidence...


  • Demarcation problem
    Demarcation problem
    The demarcation problem in the philosophy of science is about how and where to draw the lines around science. The boundaries are commonly drawn between science and non-science, between science and pseudoscience, between science and philosophy and between science and religion...

  • Holistic science

  • Junk science
    Junk science
    Junk science is a term used in U.S. political and legal disputes that brands an advocate's claims about scientific data, research, or analyses as spurious. The term may convey a pejorative connotation that the advocate is driven by political, ideological, financial, or other unscientific...

  • Pseudoscience
    Pseudoscience
    Pseudoscience is a claim, belief, or practice which is presented as scientific, but which does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status...

  • Scientific misconduct
    Scientific misconduct
    Scientific misconduct is the violation of the standard codes of scholarly conduct and ethical behavior in professional scientific research. A Lancet review on Handling of Scientific Misconduct in Scandinavian countries provides the following sample definitions: *Danish definition: "Intention or...



History, philosophy, sociology



  • Epistemology
  • Epistemic truth
    Epistemic theories of truth
    In philosophy, epistemic theories of truth are attempts to analyze the notion of truth in terms of epistemic notions such as knowledge, belief, acceptance, verification, justification, and perspective....


  • History of science
    History of science
    The history of science is the study of the historical development of human understandings of the natural world and the domains of the social sciences....

  • History of scientific method
    History of scientific method
    The history of scientific method is a history of the methodology of scientific inquiry, as differentiated from a history of science in general. The development and elaboration of rules for scientific reasoning and investigation has not been straightforward; scientific method has been the subject of...


  • Instrumentalism
    Instrumentalism
    In the philosophy of science, instrumentalism is the view that a scientific theory is a useful instrument in understanding the world. A concept or theory should be evaluated by how effectively it explains and predicts phenomena, as opposed to how accurately it describes objective...

  • Mertonian norms (Cudos)
  • Philosophy of science
    Philosophy of science
    The philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...


  • Science studies
    Science studies
    Science studies is an interdisciplinary research area that seeks to situate scientific expertise in a broad social, historical, and philosophical context. It is concerned with the history of academic disciplines, the interrelationships between science and society, and the alleged covert purposes...

  • Sociology of scientific knowledge
    Sociology of scientific knowledge
    The sociology of scientific knowledge ' is the study of science as a social activity, especially dealing "with the social conditions and effects of science, and with the social structures and processes of scientific activity."...

  • Timeline of scientific method
    Timeline of the history of scientific method
    This Timeline of the history of scientific method shows an overview of the cultural inventions that have contributed to the development of the scientific method. For a detailed account, see History of the scientific method.-BC:...



Further reading


  • Bauer, Henry H., Scientific Literacy and the Myth of the Scientific Method, University of Illinois Press, Champaign, IL, 1992
  • Beveridge, William I. B.
    William Ian Beardmore Beveridge
    Dr. William Ian Beardmore Beveridge was an Australian animal pathologist and director of the Institute of Animal Pathology, University of Cambridge. He was born in 1908 in Australia and died in 2006....

    , The Art of Scientific Investigation, Heinemann
    Heinemann (book publisher)
    Heinemann is a UK publishing house founded by William Heinemann in Covent Garden, London in 1890. On William Heinemann's death in 1920 a majority stake was purchased by U.S. publisher Doubleday. It was later acquired by commemorate Thomas Tilling in 1961...

    , Melbourne, Australia, 1950.
  • Bernstein, Richard J.
    Richard J. Bernstein
    Richard J. Bernstein is an American philosopher, the Vera List Professor of Philosophy and former dean of the graduate faculty at The New School....

    , Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis, University of Pennsylvania Press, Philadelphia, PA, 1983.

  • Brody, Baruch A. and Capaldi, Nicholas, Science: Men, Methods, Goals: A Reader: Methods of Physical Science, W. A. Benjamin, 1968
  • Brody, Baruch A., and Grandy, Richard E., Readings in the Philosophy of Science, 2nd edition, Prentice Hall, Englewood Cliffs, NJ, 1989.
  • Burks, Arthur W., Chance, Cause, Reason — An Inquiry into the Nature of Scientific Evidence, University of Chicago Press, Chicago, IL, 1977.
  • Alan Chalmers
    Alan Chalmers
    Alan Francis Chalmers has been a visiting scholar at the Flinders University Philosophy Department since 1999. For the 2007 fall semester he will be a visiting professor at the University of Pittsburgh. He was born in Bristol, England in 1939, and attained a BSc in physics at the University of...

    . What is this thing called science?
    What Is This Thing Called Science?
    What Is This Thing Called Science? is a best-selling textbook by Dr. Alan Chalmers. It is a guide to the philosophy of science which outlines the shortcomings of a naive empiricist accounts of science, and describes and assesses modern attempts to replace them...

    . Queensland University Press and Open University Press, 1976.

.
  • Dewey, John
    John Dewey
    John Dewey was an American philosopher, psychologist and educational reformer whose ideas have been influential in education and social reform. Dewey was an important early developer of the philosophy of pragmatism and one of the founders of functional psychology...

    , How We Think, D.C. Heath, Lexington, MA, 1910. Reprinted, Prometheus Books
    Prometheus Books
    Prometheus Books is a publishing company founded in August 1969 by Paul Kurtz, who also founded the Council for Secular Humanism and co-founded the Committee for Skeptical Inquiry. He is currently the chairman of all three organizations. Prometheus Books publishes a range of books, including many...

    , Buffalo, NY, 1991.
  • Earman, John
    John Earman
    John Earman is a philosopher of physics. He is currently an emeritus professor in the History and Philosophy of Science department at the University of Pittsburgh. He has also taught at UCLA, the Rockefeller University, and the University of Minnesota, and was president of the Philosophy of...

     (ed.), Inference, Explanation, and Other Frustrations: Essays in the Philosophy of Science, University of California Press, Berkeley & Los Angeles, CA, 1992.
  • Fraassen, Bas C. van
    Bas C. van Fraassen
    Bastiaan Cornelis van Fraassen is a Distinguished Professor of Philosophy at San Francisco State University, teaching courses in philosophy of science, the role of models in scientific practice and philosophical logic...

    , The Scientific Image, Oxford University Press, Oxford, UK, 1980..
  • Gadamer, Hans-Georg
    Hans-Georg Gadamer
    Hans-Georg Gadamer was a German philosopher of the continental tradition, best known for his 1960 magnum opus, Truth and Method .-Life:...

    , Reason in the Age of Science, Frederick G. Lawrence (trans.), MIT Press, Cambridge, MA, 1981.
  • Giere, Ronald N. (ed.), Cognitive Models of Science, vol. 15 in 'Minnesota Studies in the Philosophy of Science', University of Minnesota Press, Minneapolis, MN, 1992.
  • Hacking, Ian
    Ian Hacking
    Ian Hacking, CC, FRSC, FBA is a Canadian philosopher, specializing in the philosophy of science.- Life and works :...

    , Representing and Intervening, Introductory Topics in the Philosophy of Natural Science, Cambridge University Press, Cambridge, UK, 1983.
  • Heisenberg, Werner
    Werner Heisenberg
    Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

    , Physics and Beyond, Encounters and Conversations, A.J. Pomerans (trans.), Harper and Row, New York, NY 1971, pp. 63–64.
  • Holton, Gerald
    Gerald Holton
    Gerald Holton is Mallinckrodt Research Professor of Physics and Research Professor of the History of Science, Emeritus, at Harvard University.Born 1922 in Berlin, he grew up in Vienna before emigrating in 1938...

    , Thematic Origins of Scientific Thought, Kepler to Einstein, 1st edition 1973, revised edition, Harvard University Press, Cambridge, MA, 1988.
  • Kuhn, Thomas S., The Essential Tension, Selected Studies in Scientific Tradition and Change, University of Chicago Press, Chicago, IL, 1977.
  • Latour, Bruno
    Bruno Latour
    Bruno Latour is a French sociologist of science and anthropologist and an influential theorist in the field of Science and Technology Studies...

    , Science in Action, How to Follow Scientists and Engineers through Society, Harvard University Press, Cambridge, MA, 1987.
  • Losee, John, A Historical Introduction to the Philosophy of Science, Oxford University Press, Oxford, UK, 1972. 2nd edition, 1980.
  • Maxwell, Nicholas
    Nicholas Maxwell
    Nicholas Maxwell is a philosopher who has devoted much of his working life to arguing that there is an urgent need to bring about a revolution in academia so that it seeks and promotes wisdom and does not just acquire knowledge....

    , The Comprehensibility of the Universe: A New Conception of Science, Oxford University Press, Oxford, 1998. Paperback 2003.. Memoir of a researcher in the Avery–MacLeod–McCarty experiment.
  • McComas, William F.
    William McComas
    William McComas was a U.S. Representative from Virginia.Born near Pearisburg, Virginia, McComas attended private schools and Emory and Henry College, Emory, Virginia.He engaged in agricultural pursuits and in the practice of law....

    , ed. , from The Nature of Science in Science Education, pp53–70, Kluwer Academic Publishers, Netherlands 1998.
  • Misak, Cheryl J., Truth and the End of Inquiry, A Peircean Account of Truth, Oxford University Press, Oxford, UK, 1991.

  • Piattelli-Palmarini, Massimo (ed.), Language and Learning, The Debate between Jean Piaget and Noam Chomsky, Harvard University Press, Cambridge, MA, 1980.
  • Popper, Karl R., Unended Quest, An Intellectual Autobiography, Open Court, La Salle, IL, 1982.
  • Putnam, Hilary
    Hilary Putnam
    Hilary Whitehall Putnam is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science...

    , Renewing Philosophy, Harvard University Press, Cambridge, MA, 1992.
  • Rorty, Richard
    Richard Rorty
    Richard McKay Rorty was an American philosopher. He had a long and diverse academic career, including positions as Stuart Professor of Philosophy at Princeton, Kenan Professor of Humanities at the University of Virginia, and Professor of Comparative Literature at Stanford University...

    , Philosophy and the Mirror of Nature, Princeton University Press, Princeton, NJ, 1979.
  • Salmon, Wesley C.
    Wesley C. Salmon
    Wesley C. Salmon was a metaphysician and contemporary philosopher of science concerned primarily with the topics of causation and explanation....

    , Four Decades of Scientific Explanation, University of Minnesota Press, Minneapolis, MN, 1990.
  • Shimony, Abner
    Abner Shimony
    Abner Shimony is an American physicist and philosopher of science specializing in quantum theory.-Career:Shimony obtained his BA in Mathematics and Philosophy from Yale University in 1948, and an MA in Philosophy from the University of Chicago in 1950. He obtained his Ph.D...

    , Search for a Naturalistic World View: Vol. 1, Scientific Method and Epistemology, Vol. 2, Natural Science and Metaphysics, Cambridge University Press, Cambridge, UK, 1993.
  • Thagard, Paul, Conceptual Revolutions, Princeton University Press, Princeton, NJ, 1992.
  • Ziman, John
    John Ziman
    John Michael Ziman was a physicist and a humanist who worked in the area of condensed matter physics. He was an outstanding spokesman for science, and an accomplished teacher and author....

    (2000). Real Science: what it is, and what it means. Cambridge, UK: Cambridge University Press.

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