Scientific method

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Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge.^[1] To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of reasoning.^[2] The Oxford English Dictionary 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."^[3]

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 experimental 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 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 as possible, to reduce biased interpretations of results. Another basic expectation is to document, archive and share all data and methodology so they are available for careful scrutiny by other scientists, giving them the opportunity to verify results by attempting to reproduce them. This practice, called full disclosure, also allows statistical measures of the reliability of these data to be established.

Introduction to scientific method

See also: History of scientific method and Timeline of the history of scientific method

Ibn al-Haytham (Alhazen), 965–1039, Basra.

"Modern science owes its origins and present flourishing state to a new scientific method which was fashioned almost entirely by Galileo Galilei (1564-1642)" —Morris Kline[4]

Johannes Kepler (1571–1630). "Kepler shows his keen logical sense in detailing the whole process by which he finally arrived at the true orbit. This is the greatest piece of Retroductive reasoning ever performed." —C. S. Peirce, circa 1896, on Kepler's reasoning through explanatory hypotheses[5]

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:

Truth is sought for its own sake. And those who are engaged upon the quest for anything for its own sake are not interested in other things. Finding the truth is difficult, and the road to it is rough.^[6]

"Light travels through transparent bodies in straight lines only" — Alhazen in Book of Optics (1021 Arabic: Kitāb al-Manāẓir‎) as shown in a Basle 1572 Latin translation, Friedrich Risner, ed., Opticae Thesaurus Alhazeni Arabis,^[7] frontispiece showing optical phenomena: transmission of light through the atmosphere, reflection of light rays from parabolic mirrors during the defense of Syracuse by Archimedes against ships of the Roman Republic, refraction of light rays by water, and the production of colors in a rainbow.

How does light travel through transparent bodies? Light travels through transparent bodies in straight lines only.... We have explained this exhaustively in our Book of Optics. But let us now mention something to prove this convincingly: the fact that light travels in straight lines is clearly observed in the lights which enter into dark rooms through holes.... [T]he entering light will be clearly observable in the dust which fills the air.^[8]

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,^[9] to prove that light travels in a straight line.

Scientific methodology has been practiced in some form for at least one thousand years.^[10] There are difficulties in a formulaic statement of method, however. As William Whewell (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 alone;^[11] 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^[12] for scientific method was formulated (for a more formal discussion, see below):

1. Use your experience: Consider the problem and try to make sense of it. Look for previous explanations. If this is a new problem to you, then move to step 2.

2. Form a conjecture: When nothing else is yet known, try to state an explanation, to someone else, or to your notebook.

3. Deduce a prediction from that explanation: If you assume 2 is true, what consequences follow?

4. Test: Look for the opposite of each consequence in order to disprove 2. It is a logical error to seek 3 directly as proof of 2. This error is called affirming the consequent.^[13]

This model underlies the scientific revolution. One thousand years ago, Alhazen demonstrated the importance of steps 1 and 4.^[14] Galileo 1638 also showed the importance of step 4 (also called Experiment) in Two New Sciences.^[15] 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 2.^[16] (This is what Einstein meant when he said, "No amount of experimentation can ever prove me right; a single experiment can prove me wrong."^[17]) 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. Thus the likelihood of the prior observation being true is statistical in nature^[18] and would strictly require a Bayesian analysis. To overcome this uncertainty, experimental scientists must formulate a crucial experiment,^[19] in order for it to corroborate a more likely hypothesis.

In the 20th century, Ludwik Fleck (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.^[20]

DNA example

Four basic elements of scientific method are illustrated by the following example from the discovery of the structure of DNA: 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 and Watson hypothesized that the genetic material had a physical basis that was helical.[21] DNA prediction: From earlier work on tobacco mosaic virus,[22] Watson was aware of the significance of Crick's formulation of the transform of a helix.[23] Thus he was primed to recognize the significance of the X-shape in photo 51, the remarkable photograph of the X-ray diffraction image of DNA taken by Rosalind Franklin. DNA experiment: Watson saw photo 51.[24] The examples are continued in "Evaluations and iterations" with DNA-iterations.[25]

Truth and belief

Main article: Truth

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.^[26]

Beliefs and biases

Flying gallop falsified; see image below.

Belief can alter observation; human confirmation bias is a heuristic 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, self-esteem, time, and comfort can produce a readiness for new perception.^[27]

Eadweard Muybridge's studies of a horse galloping

Needham's Science and Civilization in China uses the 'flying gallop' image as an example of observation bias:^[28] 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 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 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). This is one of the reasons (mistake, confusion, inadequate instruments, etc. are others) why scientific methodology directs that hypotheses be tested in controlled conditions which can be reproduced by others. The scientific community's pursuit of experimental control and reproducibility, diminishes the effects of cognitive biases.

Certainty and myth

Any scientific theory is closely tied to empirical findings, and always remains subject to falsification if new experimental observation incompatible with it is found. That is, no theory can ever be seriously considered certain 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.^[29] 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.^[30] Imre Lakatos has noted that once a narrative is constructed its elements become easier to believe (this is called the narrative fallacy).^[31][32] 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. --^{[citation needed]}

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.^[33] Yet there is a preference in the scientific community for new, surprising statements, and the search for evidence that the new is true.^[1] Goldhaber & Nieto 2010, p. 941 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 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 sciences than social sciences. Nonetheless, the cycle of formulating hypotheses, testing and analyzing the results, and formulating new hypotheses, will resemble the cycle described below.

Four essential elements^[34][35][36] of a scientific method^[37] are iterations,^[38][39] recursions,^[40] interleavings, or orderings of the following:

• Characterizations (observations,^[41] definitions, and measurements of the subject of inquiry)
• Hypotheses^[42][43] (theoretical, hypothetical explanations of observations and measurements of the subject)^[44]
• Predictions (reasoning including logical deduction^[45] from the hypothesis or theory)
• Experiments^[46] (tests of all of the above)

Each element of a scientific method is subject to peer review 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 as "the scientific method".^[47]

The scientific method is not a single recipe: it requires intelligence, imagination, and creativity.^[48] 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:^[49]

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 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,^[50] it should also be noted that a number of philosophers, historians and sociologists of science (perhaps most notably Paul Feyerabend) 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, instrumentalism, and utility:

The essential elements of a scientific method are operations, observations, models, and a utility function for evaluating models.^{[51][not in citation given]}

• Operation - Some action done to the system being investigated
• Observation - What happens when the operation is done to the system
• Model - A fact, hypothesis, theory, 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, on the Principle of Parsimony more commonly known as Occam's Razor.

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 conjectured, correctly, that St. Elmo's fire was electrical in nature, but it has taken a long series of experiments and theoretical changes to establish this. While seeking the pertinent properties of the subjects, careful thought may also entail some definitions and observations; the observations often demand careful measurements and/or counting.

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

"I am not accustomed to saying anything with certainty after only one or two observations."—Andreas Vesalius (1546) [52]

Uncertainty

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

Definition

Measurements demand the use of operational definitions of relevant quantities. That is, a scientific quantity is described or defined by how it is measured, as opposed to some more vague, inexact or "idealized" definition. For example, 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 usage. For example, mass and weight overlap in meaning in common discourse, but have distinct meanings in mechanics. Scientific quantities are often characterized by their units of measure which can later be described in terms of conventional physical units when communicating the work.

New theories are sometimes developed after realizing certain terms have not previously been sufficiently clearly defined. For example, Albert Einstein's first paper on relativity begins by defining simultaneity and the means for determining length. These ideas were skipped over by Isaac Newton with, "I do not define time, space, place and motion, as being well known to all." Einstein's paper then demonstrates that they (viz., absolute time and length independent of motion) were approximations. Francis Crick cautions us that when characterizing a subject, however, it can be premature to define something when it remains ill-understood.^[53] In Crick's study of consciousness, he actually found it easier to study awareness in the visual system, rather than to study free will, for example. His cautionary example was the gene; the gene was much more poorly understood before Watson and Crick's pioneering discovery of the structure of DNA; it would have been counterproductive to spend much time on the definition of the gene, before them.

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, and that DNA contained genetic information (Oswald Avery's transforming principle).^[54] But the mechanism of storing genetic information (i.e., genes) in DNA was unclear. Researchers in Bragg's laboratory at Cambridge University made X-ray diffraction pictures of various molecules, starting with crystals of salt, and proceeding to more complicated substances. Using clues painstakingly assembled over decades, beginning with its chemical composition, it was determined that it should be possible to characterize the physical structure of DNA, and the X-ray images would be the vehicle.^[55] ..2. DNA-hypotheses

Another example: precession of Mercury

Precession of the perihelion (exaggerated)

The characterization element can require extended and extensive study, even centuries. It took thousands of years of measurements, from the Chaldean, Indian, Persian, Greek, Arabic and European astronomers, to fully record the motion of planet Earth. Newton was able to include those measurements into consequences of his laws of motion. But the perihelion of the planet Mercury's orbit exhibits a precession that cannot be fully explained by Newton's laws of motion (see diagram to the right), though it took quite some time to realize this. The observed difference for Mercury's precession 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. His relativistic calculations matched observation much more closely than did Newtonian theory (the difference is approximately 43 arc-seconds per century), .

Hypothesis development

Main article: Hypothesis formation

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

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

Scientists are free to use whatever resources they have — their own creativity, ideas from other fields, induction, Bayesian inference, and so on — to imagine possible explanations for a phenomenon under study. Charles Sanders Peirce, borrowing a page from Aristotle (Prior Analytics, 2.25) described the incipient stages of inquiry, instigated by the "irritation of doubt" to venture a plausible guess, as abductive reasoning. The history of science is filled with stories of scientists claiming a "flash of inspiration", or a hunch, which then motivated them to look for evidence to support or refute their idea. Michael Polanyi made such creativity the centerpiece of his discussion of methodology.

William Glen 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.^[56]

In general scientists tend to look for theories that are "elegant" or "beautiful". 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 serves as a rule of thumb for choosing the most desirable amongst a group of equally explanatory hypotheses.

DNA-hypotheses

Linus Pauling proposed that DNA might be a triple helix.^[57] This hypothesis was also considered by Francis Crick and James D. Watson but discarded. When Watson and Crick learned of Pauling's hypothesis, they understood from existing data that Pauling was wrong^[58] 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

Main article: Prediction in science

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

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, Francis Crick, and others hypothesized that DNA had a helical structure. This implied that DNA's X-ray diffraction pattern would be 'x shaped'.^[59][60] This prediction followed from the work of Cochran, Crick and Vand^[23] (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, writing "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material".^[61] ..4. DNA-experiments

Another example: general relativity

Einstein's prediction (1907): Light bends in a gravitational field

Einstein's theory of General Relativity makes several specific predictions about the observable structure of space-time, such as that light bends in a gravitational field, and that the amount of bending depends in a precise way on the strength of that gravitational field. Arthur Eddington's observations made during a 1919 solar eclipse supported General Relativity rather than Newtonian gravitation.^[62]

Experiments

Main article: Experiment

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.^[63] Factor analysis 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 study or an archaeological excavation. Even taking a plane from New York to Paris is an experiment which tests the aerodynamical 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 (190-120 BCE), when determining a value for the precession of the Earth, while controlled experiments can be seen in the works of Jābir ibn Hayyān (721-815 CE), al-Battani (853–929) and Alhazen (965-1039).^[64]

DNA-experiments

Watson and Crick showed an initial (and incorrect) proposal for the structure of DNA to a team from Kings College - Rosalind Franklin, Maurice Wilkins, and Raymond Gosling. Franklin immediately spotted the flaws which concerned the water content. Later Watson saw Franklin's detailed X-ray diffraction images which showed an X-shape and was able to confirm the structure was helical.^[24][65] 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, 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,^[66][67][68] Watson and Crick were able to infer the essential structure of DNA by concrete modeling of the physical shapes of the nucleotides which comprise it.^[25][69] They were guided by the bond lengths which had been deduced by Linus Pauling and by Rosalind Franklin's X-ray diffraction images. ..DNA Example

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 was killed by ball lightning (1753) when attempting to replicate the 1752 kite-flying experiment of Benjamin Franklin.^[70]

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

Models of scientific inquiry

Main article: Models of scientific inquiry

Classical model

The classical model of scientific inquiry derives from Aristotle,^[71] who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy.

Pragmatic model

See also: Pragmatic theory of truth

In 1877,^[72] Charles Sanders Peirce ( /ˈpɜrs/ 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.^[73] 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 paradigms 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 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,^[74] 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.^[75] 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.^[72][76]

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.^[77] 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.^[78] As inference, "logic is rooted in the social principle" since it depends on a standpoint that is, in a sense, unlimited.^[79]

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"^[80] except as otherwise noted):

1. Abduction (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.^[81] Coordinative method leads from abducing a plausible hypothesis to judging it for its testability^[82] and for how its trial would economize inquiry itself.^[83] Peirce calls his pragmatism "the logic of abduction".^[84] His pragmatic maxim 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".^[77] 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), breadth, and incomplexity.^[85] 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.^[83]

2. Deduction. 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, Euclidean in procedure. Explicit deduction of hypothesis's consequences as predictions, for induction to test, about evidence to be found. Corollarial or, if needed, Theorematic.

3. Induction. The long-run validity of the rule of induction is deducible from the principle (presuppositional to reasoning in general^[77]) that the real is only the object of the final opinion to which adequate investigation would lead;^[86] 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 weightings of qualities or characters;^[87] 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, such as artificial intelligence, machine learning, computational learning theory, inferential statistics, and knowledge representation, 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, logical deduction, and empirical testing. Some of these applications draw on measures of complexity from algorithmic information theory to guide the making of predictions from prior distributions of experience, for example, see the complexity measure called the speed prior 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. 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, 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 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" can interfere with open and fair deliberation of some new research.^[88]

Documentation and replication

Main article: Reproducibility

Sometimes experimenters may make systematic errors during their experiments, unconsciously veer from a scientific method (Pathological science) 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 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. 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, 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

Further information: Rhetoric of science

The primary constraints on contemporary western science are:

• Publication, i.e. Peer review
• Resources (mostly funding)

It has not always been like this: in the old days of the "gentleman scientist" 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.

Philosophy and sociology of science

Main articles: Philosophy of science and Sociology of science

Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science, and the ethic that is implicit in science. There are basic assumptions derived from philosophy that form the base of the scientific method - namely, that reality is objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world. These assumptions from methodological naturalism form the basis on which science is grounded. Logical Positivist, empiricist, falsificationist, and other theories have claimed to give a definitive account of the logic of science, but each has in turn been criticized.

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

Norwood Russell Hanson, Imre Lakatos and Thomas Kuhn have done extensive work on the "theory laden" character of observation. Hanson (1958) first coined the term for the idea that all observation is dependent on the conceptual framework of the observer, using the concept of gestalt to show how preconceptions can affect both observation and description.^[89] He opens Chapter 1 with a discussion of the Golgi bodies and their initial rejection as an artefact of staining technique, and a discussion of Brahe and Kepler observing the dawn and seeing a "different" sun rise despite the same physiological phenomenon. Kuhn ^[90] and Feyerabend ^[91] 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".^[92]

Paul Feyerabend similarly examined the history of science, and was led to deny that science is genuinely a methodological process. In his book Against Method he argues that scientific progress is not the result of applying any particular method. In essence, he says that for any specific method or norm of science, one can find a historic episode where violating it has contributed to the progress of science. Thus, if believers in a scientific method wish to express a single universally valid rule, Feyerabend jokingly suggests, it should be 'anything goes'.^[93] Criticisms such as his led to the strong programme, a radical approach to the sociology of science.

Highly controlled experimentation allows researchers to catch their mistakes, but it also makes anomalies (which no one knew to look for) easier to see

In his 1958 book, Personal Knowledge, chemist and philosopher Michael Polanyi (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 critiques of science have themselves been the subject of intense controversy. This ongoing debate, known as the science wars, is the result of conflicting values and assumptions between the postmodernist and realist camps. Whereas postmodernists assert that scientific knowledge is simply another discourse (note that this term has special meaning in this context) and not representative of any form of fundamental truth, realists in the scientific community maintain that scientific knowledge does reveal real and fundamental truths about reality. Many books have been written by scientists which take on this problem and challenge the assertions of the postmodernists while defending science as a legitimate method of deriving truth.^[94]

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.^[95] Louis Pasteur is credited with the famous saying that "Luck favours the prepared mind", but some psychologists have begun to study what it means to be 'prepared for luck' in the scientific context. Research is showing that scientists are taught various heuristics that tend to harness chance and the unexpected.^[95][96] 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.^[97]

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.^[95][96]

History

Main article: History of scientific method

See also: Timeline of the history of scientific method

Aristotle, 384 BC–322 BC. "As regards his method, Aristotle is recognized as the inventor of scientific method because of his refined analysis of logical implications contained in demonstrative discourse, which goes well beyond natural logic and does not owe anything to the ones who philosophized before him."—Riccardo Pozzo^[98]

The development of the scientific method is inseparable from the history of science itself. Ancient Egyptian documents describe empirical methods in astronomy,^[99] mathematics,^[100] and medicine.^[101] The ancient Greek philosopher Thales 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 by Plato was an important step towards the scientific method. Empiricism seems to have been formalized by Aristotle, who believed that universal truths could be reached via induction.

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), but the first clear instances of an experimental scientific method seem to have been developed by Islamic scientists who introduced the use of experimentation and quantification within a generally empirical orientation. For example, Alhazen performed optical and physiological experiments, reported in his manifold works, the most famous being Book of Optics (1021).^{[102][unreliable source?]} The modern scientific method crystallized no later than in the 17th and 18th centuries. In his work Novum Organum (1620) — a reference to Aristotle's Organon — Francis Bacon outlined a new system of logic to improve upon the old philosophical process of syllogism.^[103] Then, in 1637, René Descartes established the framework for a scientific method's guiding principles in his treatise, Discourse on Method. 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.^[104]

Grosseteste was "the principal figure" in bringing about "a more adequate method of scientific inquiry" by which "medieval scientists were able eventually to outstrip their ancient European and Muslim teachers" (Dales 1973:62). ... His thinking influenced Roger Bacon, who spread Grosseteste's ideas from Oxford to the University of Paris during a visit there in the 1240s. From the prestigious universities in Oxford and Paris, the new experimental science spread rapidly throughout the medieval universities: "And so it went to Galileo, William Gilbert, Francis Bacon, William Harvey, Descartes, Robert Hooke, Newton, Leibniz, and the world of the seventeenth century" (Crombie 1962:15). So it went to us also.

— Hugh G. Gauch, 2003.^[105]

Roger Bacon (c.1214–1294) is sometimes credited as one of the earliest European advocates of the modern scientific method inspired by the works of Aristotle.^[106]

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, 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, deductive, and inductive 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 argued that there is no such thing as inductive reasoning.^[107] All inferences ever made, including in science, are purely^[108] 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 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".^[109] 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. 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.^[109] In contrast to empiricist-inductivist views, he welcomed metaphysics and philosophical discussion and even gave qualified support to myths^[110] and pseudosciences.^[111] Popper's view has become known as critical rationalism.

Relationship with mathematics

Science is the process of gathering, comparing, and evaluating proposed models against observables. A model can be a simulation, mathematical or chemical formula, or set of proposed steps. Science is like mathematics in that researchers in both disciplines 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. 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.^[112]

Mathematical work and scientific work can inspire each other.^[113] For example, the technical concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture has been proven using time as a mathematical concept in which objects can flow (see Ricci flow).

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

George Pólya's work on problem solving,^[114] the construction of mathematical proofs, and heuristic^[115][116] 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	Scientific method
1	Understanding	Characterization from experience and observation
2	Analysis	Hypothesis: a proposed explanation
3	Synthesis	Deduction: prediction from the hypothesis
4	Review/Extend	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,^[117] involves free and heuristic construction of plausible arguments, working backward from the goal, and devising a plan for constructing the proof; synthesis is the strict Euclidean exposition of step-by-step details^[118] of the proof; review involves reconsidering and re-examining the result and the path taken to it.

Gauss, when asked how he came about his theorems, once replied "durch planmässiges Tattonieren" (through systematic palpable experimentation).^[119]

Imre Lakatos argued that mathematicians actually use contradiction, criticism and revision as principles for improving their work.^[120]

See also

Confirmability Contingency Falsifiability Hypothesis Hypothesis testing Inquiry Information theory

Logic Abductive reasoning Deductive reasoning Inductive reasoning Inference Tautology

Methodology Baconian method Empirical method Historical method Philosophical method Phronetic method Scholarly method Strong inference Mathematics OGHET

Operationalization Quantitative research Reproducibility Research Social research Statistics Testability Theory Verification and Validation

Problems and issues

Induction Problem of induction Occam's razor Skeptical hypotheses

Poverty of the stimulus Reference class problem Underdetermination

Demarcation problem Holistic science

Junk science Pseudoscience Scientific misconduct

History, philosophy, sociology

Epistemology Epistemic truth

History of science History of scientific method

Instrumentalism Mertonian norms (Cudos) Philosophy of science

Science studies Sociology of scientific knowledge Timeline of scientific method

Notes

1. ^ ^{a b} Goldhaber & Nieto 2010, p. 940
2. ^ "[4] Rules for the study of natural philosophy", Newton 1999, pp. 794–6, from Book 3, The System of the World.
3. ^ Oxford English Dictionary - entry for scientific.
4. ^ Morris Kline (1985) Mathematics for the nonmathematician. Courier Dover Publications. p. 284. ISBN 0-486-24823-2
5. ^ Peirce, C. S., Collected Papers v. 1, paragraph 74.
6. ^ Alhazen (Ibn Al-Haytham) Critique of Ptolemy, translated by S. Pines, Actes X Congrès internationale d'histoire des sciences, Vol I Ithaca 1962, as quoted in Sambursky 1974, p. 139
7. ^ Edward Grant (1974), A source book in medieval science Volume one Cambridge MA: Harvard University Press p.392
8. ^ Alhazen, translated into English from German by M. Schwarz, from "Abhandlung über das Licht", J. Baarmann (ed. 1882) Zeitschrift der Deutschen Morgenländischen Gesellschaft Vol 36 as quoted in Sambursky 1974, p. 136
9. ^ as quoted in Sambursky 1974, p. 136
10. ^ "Truth is sought for its own sake. And those who are engaged upon the quest for anything for its own sake are not interested in other things. Finding the truth is difficult, and the road to it is rough."—Alhazen (Ibn Al-Haytham 965-c.1040) Critique of Ptolemy, translated by S. Pines, Actes X Congrès internationale d'histoire des sciences, Vol I Ithaca 1962, as quoted in Sambursky 1974, p. 139. (This quotation is from Alhazen's critique of Ptolemy's books Almagest, Planetary Hypotheses, and Optics as translated into English by A. Mark Smith.)
11. ^ "...the statement of a law—A depends on B—always transcends experience." —Born 1949, p. 6
12. ^ Godfrey-Smith 2003 p. 236.
13. ^ Taleb 2007 e.g., p. 58, devotes his chapter 5 to the error of confirmation.
14. ^ "How does light travel through transparent bodies? Light travels through transparent bodies in straight lines only.... We have explained this exhaustively in our Book of Optics. But let us now mention something to prove this convincingly: the fact that light travels in straight lines is clearly observed in the lights which enter into dark rooms through holes.... [T]he entering light will be clearly observable in the dust which fills the air. —Alhazen, translated into English from German by M. Schwarz, from "Abhandlung über das Licht", J. Baarmann (ed. 1882) Zeitschrift der Deutschen Morgenländischen Gesellschaft Vol 36 as quoted in Sambursky 1974, p. 136.
    • 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, as quoted in Sambursky 1974, p. 136 to prove that light travels in a straight line.
    • David Hockney, (2001, 2006) in Secret Knowledge: rediscovering the lost techniques of the old masters ISBN 0-14-200512-6 (expanded edition) cites Alhazen several times as the likely source for the portraiture technique using the camera obscura, which Hockney rediscovered with the aid of an optical suggestion from Charles M. Falco. Kitab al-Manazir, which is Alhazen's Book of Optics, at that time denoted Opticae Thesaurus, Alhazen Arabis, was translated from Arabic into Latin for European use as early as 1270. Hockney cites Friedrich Risner's 1572 Basle edition of Opticae Thesaurus. Hockney quotes Alhazen as the first clear description of the camera obscura in Hockney, p. 240.
15. ^ Galilei, Galileo (M.D.C.XXXVIII), Discorsi e Dimonstrazioni Matematiche, intorno a due nuoue scienze, Leida: Apresso gli Elsevirri, ISBN 0-486-60099-8 , Dover reprint of the 1914 Macmillan translation by Henry Crew and Alfonso de Salvio of Two New Sciences, Galileo Galilei Linceo (1638). Additional publication information is from the collection of first editions of the Library of Congress surveyed by Bruno 1989, pp. 261–264.
16. ^ "I believe that we do not know anything for certain, but everything probably." —Christiaan Huygens, Letter to Pierre Perrault, 'Sur la préface de M. Perrault de son traité del'Origine des fontaines' [1763], Oeuvres Complétes de Christiaan Huygens (1897), Vol. 7, 298. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 163. Quotation selected by Bynum & Porter 2005, p. 317 Huygens 317#4.
17. ^ As noted by Alice Calaprice (ed. 2005) The New Quotable Einstein Princeton University Press and Hebrew University of Jerusalem, ISBN 0-691-12074-9 p. 291. Calaprice denotes this not as an exact quotation, but as a paraphrase of a translation of A. Einstein's "Induction and Deduction". Collected Papers of Albert Einstein 7 Document 28. Volume 7 is The Berlin Years: Writings, 1918-1921. A. Einstein; M. Janssen, R. Schulmann, et al., eds.
18. ^ Murzi, Mauro (2001, 2008), "Carl Gustav Hempel (1905—1997)", Internet Encyclopedia of Philosophy.
19. ^ Poincaré 1905 p.142 notes that Francis Bacon introduced the term; on a related note, Ørsted introduced the term 'thought experiment'; of course, Galileo, a contemporary of Bacon, had previously made liberal use of these concepts in his writings centuries earlier than Poincaré or Ørsted.
20. ^ Fleck 1979, pp. xxvii-xxviii
21. ^ October, 1951. as noted in McElheny 2004, p. 40:"That's what a helix should look like!" Crick exclaimed in delight (This is the Cochran-Crick-Vand&Stokes theory of the transform of a helix).
22. ^ June, 1952. as noted in McElheny 2004, p. 43: Watson had succeeded in getting X-ray pictures of TMV showing a helical structure
23. ^ ^{a b} Cochran W, Crick FHC and Vand V. (1952) "The Structure of Synthetic Polypeptides. I. The Transform of Atoms on a Helix", Acta Cryst., 5, 581-586.
24. ^ ^{a b} Friday, January 30, 1953. Tea time. as noted in McElheny 2004, p. 52: Franklin confronts Watson and his paper - "Of course it [Pauling's pre-print] is wrong. DNA is not a helix." Watson ran away from Franklin and into Wilkins; in Wilkins' office, Watson saw photo 51. Watson immediately recognizes the diffraction pattern of a helical structure.
25. ^ ^{a b} Saturday, February 28, 1953, as noted in McElheny 2004, pp. 57–59: Watson found the base pairing mechanism which explained Chargaff's rules using his cardboard models.
26. ^ "People start off with a belief and a prejudice—we all do. And the job of science is to set that aside to get to the truth." —Simon Singh, as quoted in Wired (August 30, 2010) interview by Robert Capps
27. ^ "Observation and experiment are subject to a very popular myth. ... The knower is seen as a ... Julius Caesar winning his battles according to ... formula. Even research workers will admit that the first observation may have been a little imprecise, whereas the second and third were 'adjusted to the facts' ... until tradition, education, and familiarity have produced a readiness for stylized (that is directed and restricted) perception and action; until an answer becomes largely pre-formed in the question, and a decision confined merely to 'yes' or 'no' or perhaps to a numerical determination; until methods and apparatus automatically carry out the greatest part of the mental work for us." Ludwik Fleck labels this thought style(Denkstil). Fleck 1979, p. 84.
28. ^ Needham & Wang 1954 p.166 shows how the 'flying gallop' image propagated from China to the West.
29. ^ Stanovich, Keith E. (2007). How to Think Straight About Psychology. Boston: Pearson Education. pg 123
30. ^ "A myth is a belief given uncritical acceptance by members of a group ..." —Weiss, Business Ethics p. 15, as cited by Ronald R. Sims (2003) Ethics and corporate social responsibility: why giants fall p.21
31. ^ Imre Lakatos (1976), Proofs and Refutations. Taleb 2007, p. 72 lists ways to avoid narrative fallacy and confirmation bias.
32. ^ For more on the narrative fallacy, see also Fleck 1979, p. 27: "Words and ideas are originally phonetic and mental equivalences of the experiences coinciding with them. ... Such proto-ideas are at first always too broad and insufficiently specialized. ... Once a structurally complete and closed system of opinions consisting of many details and relations has been formed, it offers enduring resistance to anything that contradicts it."
33. ^ Brody 1993, pp. 44–45
34. ^ See the hypothethico-deductive method, for example, Godfrey-Smith 2003, p. 236.
35. ^ Jevons 1874, pp. 265–6.
36. ^ pp.65,73,92,398 —Andrew J. Galambos, Sic Itur ad Astra ISBN 0-88078-004-5(AJG learned scientific method from Felix Ehrenhaft
37. ^ Galileo 1638, pp. v-xii,1–300
38. ^ Brody 1993, pp. 10–24 calls this the "epistemic cycle": "The epistemic cycle starts from an initial model; iterations of the cycle then improve the model until an adequate fit is achieved."
39. ^ Iteration example: Chaldean astronomers such as Kidinnu compiled astronomical data. Hipparchus was to use this data to calculate the precession of the Earth's axis. Fifteen hundred years after Kidinnu, Al-Batani, born in what is now Turkey, would use the collected data and improve Hipparchus' value for the precession of the Earth's axis. Al-Batani's value, 54.5 arc-seconds per year, compares well to the current value of 49.8 arc-seconds per year (26,000 years for Earth's axis to round the circle of nutation).
40. ^ Recursion example: the Earth is itself a magnet, with its own North and South Poles William Gilbert (in Latin 1600) De Magnete, or On Magnetism and Magnetic Bodies. Translated from Latin to English, selection by Moulton & Schifferes 1960, pp. 113–117. Gilbert created a terrella, a lodestone ground into a spherical shape, which served as Gilbert's model for the Earth itself, as noted in Bruno 1989, p. 277.
41. ^ "The foundation of general physics ... is experience. These ... everyday experiences we do not discover without deliberately directing our attention to them. Collecting information about these is observation." —Hans Christian Ørsted("First Introduction to General Physics" ¶13, part of a series of public lectures at the University of Copenhagen. Copenhagen 1811, in Danish, printed by Johan Frederik Schulz. In Kirstine Meyer's 1920 edition of Ørsted's works, vol.III pp. 151-190. ) "First Introduction to Physics: the Spirit, Meaning, and Goal of Natural Science". Reprinted in German in 1822, Schweigger's Journal für Chemie und Physik 36, pp.458-488, as translated in Ørsted 1997, p. 292
42. ^ "When it is not clear under which law of nature an effect or class of effect belongs, we try to fill this gap by means of a guess. Such guesses have been given the name conjectures or hypotheses." —Hans Christian Ørsted(1811) "First Introduction to General Physics" as translated in Ørsted 1997, p. 297.
43. ^ "In general we look for a new law by the following process. First we guess it. ...", —Feynman 1965, p. 156
44. ^ "... the statement of a law - A depends on B - always transcends experience."—Born 1949, p. 6
45. ^ "The student of nature ... regards as his property the experiences which the mathematician can only borrow. This is why he deduces theorems directly from the nature of an effect while the mathematician only arrives at them circuitously." —Hans Christian Ørsted(1811) "First Introduction to General Physics" ¶17. as translated in Ørsted 1997, p. 297.
46. ^ Salviati speaks: "I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of, say, 100 cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits." Two New Sciences (1638) —Galileo 1638, pp. 61–62. A more extended quotation is referenced by Moulton & Schifferes 1960, pp. 80–81.
47. ^ In the inquiry-based education paradigm, the stage of "characterization, observation, definition, …" is more briefly summed up under the rubric of a Question
48. ^ "To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science." —Einstein & Infeld 1938, p. 92.
49. ^ Crawford S, Stucki L (1990), "Peer review and the changing research record", "J Am Soc Info Science", vol. 41, pp 223-228
50. ^ See, e.g., Gauch 2003, esp. chapters 5-8
51. ^ Cartwright, Nancy (1983), How the Laws of Physics Lie. Oxford: Oxford University Press. ISBN 0-19-824704-4
52. ^ Andreas Vesalius, Epistola, Rationem, Modumque Propinandi Radicis Chynae Decocti (1546), 141. Quoted and translated in C.D. O'Malley, Andreas Vesalius of Brussels, (1964), 116. As quoted by Bynum & Porter 2005, p. 597: Andreas Vesalius,597#1.
53. ^ Crick, Francis (1994), The Astonishing Hypothesis ISBN 0-684-19431-7 p.20
54. ^ McCarty1985
55. ^ McElheny 2004 p.34
56. ^ Glen 1994, pp. 37–38.
57. ^ "The structure that we propose is a three-chain structure, each chain being a helix" — Linus Pauling, as quoted on p. 157 by Horace Freeland Judson (1979), The Eighth Day of Creation ISBN 0-671-22540-5
58. ^ McElheny 2004, pp. 49–50: January 28, 1953 - Watson read Pauling's pre-print, and realized that in Pauling's model, DNA's phosphate groups had to be un-ionized. But DNA is an acid, which contradicts Pauling's model.
59. ^ June, 1952. as noted in McElheny 2004, p. 43: Watson had succeeded in getting X-ray pictures of TMV showing a diffraction pattern consistent with the transform of a helix.
60. ^ Watson did enough work on Tobacco mosaic virus to produce the diffraction pattern for a helix, per Crick's work on the transform of a helix. pp. 137-138, Horace Freeland Judson (1979) The Eighth Day of Creation ISBN 0-671-22540-5
61. ^ McElheny 2004 p.68: Nature April 25, 1953.
62. ^ In March 1917, the Royal Astronomical Society announced that on May 29, 1919, the occasion of a total eclipse of the sun would afford favorable conditions for testing Einstein's General theory of relativity. One expedition, to Sobral, Ceará, Brazil, and Eddington's expedition to the island of Principe yielded a set of photographs, which, when compared to photographs taken at Sobral and at Greenwich Observatory showed that the deviation of light was measured to be 1.69 arc-seconds, as compared to Einstein's desk prediction of 1.75 arc-seconds. — Antonina Vallentin (1954), Einstein, as quoted by Samuel Rapport and Helen Wright (1965), Physics, New York: Washington Square Press, pp 294-295.
63. ^ Mill, John Stuart, "A System of Logic", University Press of the Pacific, Honolulu, 2002, ISBN 1-4102-0252-6.
64. ^ al-Battani, De Motu Stellarum translation from Arabic to Latin in 1116, as cited by "Battani, al-" (c.858-929) Encyclopaedia Britannica, 15th. ed. Al-Battani is known for his accurate observations at al-Raqqah in Syria, beginning in 877. His work includes measurement of the annual precession of the equinoxes.
65. ^ "The instant I saw the picture my mouth fell open and my pulse began to race." —Watson 1968, p. 167 Page 168 shows the X-shaped pattern of the B-form of DNA, clearly indicating crucial details of its helical structure to Watson and Crick.
    • McElheny 2004 p.52 dates the Franklin-Watson confrontation as Friday, January 30, 1953. Later that evening, Watson urges Wilkins to begin model-building immediately. But Wilkins agrees to do so only after Franklin's departure.
66. ^ McElheny 2004 p.53: The weekend (January 31-February 1) after seeing photo 51, Watson informed Bragg of the X-ray diffraction image of DNA in B form. Bragg gave them permission to restart their research on DNA (that is, model building).
67. ^ McElheny 2004 p.54: On Sunday February 8, 1953, Maurice Wilkes gave Watson and Crick permission to work on models, as Wilkes would not be building models until Franklin left DNA research.
68. ^ McElheny 2004 p.56: Jerry Donohue, on sabbatical from Pauling's lab and visiting Cambridge, advises Watson that textbook form of the base pairs was incorrect for DNA base pairs; rather, the keto form of the base pairs should be used instead. This form allowed the bases' hydrogen bonds to pair 'unlike' with 'unlike', rather than to pair 'like' with 'like', as Watson was inclined to model, on the basis of the textbook statements. On February 27, 1953, Watson was convinced enough to make cardboard models of the nucleotides in their keto form.
69. ^ "Suddenly I became aware that an adenine-thymine pair held together by two hydrogen bonds was identical in shape to a guanine-cytosine pair held together by at least two hydrogen bonds. ..." —Watson 1968, pp. 194–197.
    • McElheny 2004 p.57 Saturday, February 28, 1953, Watson tried 'like with like' and admited these base pairs didn't have hydrogen bonds that line up. But after trying 'unlike with unlike', and getting Jerry Donohue's approval, the base pairs turned out to be identical in shape (as Watson stated above in his 1968 Double Helix memoir quoted above). Watson now felt confident enough to inform Crick. (Of course, 'unlike with unlike' increases the number of possible codons, if this scheme were a genetic code.)
70. ^ See, e.g., Physics Today, 59(1), p42. Richmann electrocuted in St. Petersburg (1753)
71. ^ Aristotle, "Prior Analytics", Hugh Tredennick (trans.), pp. 181-531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
72. ^ ^{a b} Peirce (1877), "The Fixation of Belief", Popular Science Monthly, v. 12, pp. 1–15. Reprinted often, including (Collected Papers of Charles Sanders Peirce v. 5, paragraphs 358–87), (The Essential Peirce, v. 1, pp. 109–23). Peirce.org Eprint. Wikisource Eprint.
73. ^ "What one does not in the least doubt one should not pretend to doubt; but a man should train himself to doubt," said Peirce in a brief intellectual autobiography; see Ketner, Kenneth Laine (2009) "Charles Sanders Peirce: Interdisciplinary Scientist" in The Logic of Interdisciplinarity). Peirce held that actual, genuine doubt originates externally, usually in surprise, but also that it is to be sought and cultivated, "provided only that it be the weighty and noble metal itself, and no counterfeit nor paper substitute"; in "Issues of Pragmaticism", The Monist, v. XV, n. 4, pp. 481-99, see p. 484, and p. 491. (Reprinted in Collected Papers v. 5, paragraphs 438-63, see 443 and 451).
74. ^ Peirce (1898), "Philosophy and the Conduct of Life", Lecture 1 of the Cambridge (MA) Conferences Lectures, published in Collected Papers v. 1, paragraphs 616-48 in part and in Reasoning and the Logic of Things, Ketner (ed., intro.) and Putnam (intro., comm.), pp. 105-22, reprinted in Essential Peirce v. 2, pp. 27-41.
75. ^ Peirce (1899), "F.R.L." [First Rule of Logic], Collected Papers v. 1, paragraphs 135-40, Eprint
76. ^ Collected Papers v. 5, in paragraph 582, from 1898:

    ... [rational] inquiry of every type, fully carried out, has the vital power of self-correction and of growth. This is a property so deeply saturating its inmost nature that it may truly be said that there is but one thing needful for learning the truth, and that is a hearty and active desire to learn what is true.

77. ^ ^{a b c} Peirce (1877), "How to Make Our Ideas Clear", Popular Science Monthly, v. 12, pp. 286–302. Reprinted often, including Collected Papers v. 5, paragraphs 388–410, Essential Peirce v. 1, pp. 124–41. ArisbeEprint. Wikisource Eprint.
78. ^ Peirce (1868), "Some Consequences of Four Incapacities", Journal of Speculative Philosophy v. 2, n. 3, pp. 140–57. Reprinted Collected Papers v. 5, paragraphs 264–317, The Essential Peirce v. 1, pp. 28–55, and elsewhere. Arisbe Eprint
79. ^ Peirce (1878), "The Doctrine of Chances", Popular Science Monthly v. 12, pp. 604-15, see pp. 610-11 via Internet Archive. Reprinted Collected Papers v. 2, paragraphs 645-68, Essential Peirce v. 1, pp. 142-54. "...death makes the number of our risks, the number of our inferences, finite, and so makes their mean result uncertain. The very idea of probability and of reasoning rests on the assumption that this number is indefinitely great. .... ...logicality inexorably requires that our interests shall not be limited. .... Logic is rooted in the social principle."
80. ^ Peirce (1908), "A Neglected Argument for the Reality of God", Hibbert Journal v. 7, pp. 90-112. Wikisource:A Neglected Argument for the Reality of God with added notes. Reprinted with previously unpublished part, Collected Papers v. 6, paragraphs 452-85, The Essential Peirce v. 2, pp. 434-50, and elsewhere.
81. ^ Peirce (c. 1906), "PAP (Prolegomena for an Apology to Pragmatism)" (Manuscript 293, not the like-named article), The New Elements of Mathematics (NEM) 4:319-320, see first quote under "Abduction" at Commens Dictionary of Peirce's Terms.
82. ^ Peirce, Carnegie application (L75, 1902), New Elements of Mathematics v. 4, pp. 37-38:

    For it is not sufficient that a hypothesis should be a justifiable one. Any hypothesis which explains the facts is justified critically. But among justifiable hypotheses we have to select that one which is suitable for being tested by experiment.

83. ^ ^{a b} Peirce (1902), Carnegie application, see MS L75.329-330, from Draft D of Memoir 27:

    Consequently, to discover is simply to expedite an event that would occur sooner or later, if we had not troubled ourselves to make the discovery. Consequently, the art of discovery is purely a question of economics. The economics of research is, so far as logic is concerned, the leading doctrine with reference to the art of discovery. Consequently, the conduct of abduction, which is chiefly a question of heuretic and is the first question of heuretic, is to be governed by economical considerations.

84. ^ Peirce (1903), "Pragmatism — The Logic of Abduction", Collected Papers v. 5, paragraphs 195-205, especially 196. Eprint.
85. ^ Peirce, "On the Logic of Drawing Ancient History from Documents", Essential Peirce v. 2, see pp. 107-9. On Twenty Questions, p. 109:

    Thus, twenty skillful hypotheses will ascertain what 200,000 stupid ones might fail to do.

86. ^ Peirce (1878), "The Probability of Induction", Popular Science Monthly, v. 12, pp. 705-18, see 718 Google Books; 718 via Internet Archive. Reprinted often, including (Collected Papers v. 2, paragraphs 669-93), (The Essential Peirce v. 1, pp. 155-69).
87. ^ Peirce (1905 draft "G" of "A Neglected Argument"), "Crude, Quantitative, and Qualitative Induction", Collected Papers v. 2, paragraphs 755–760, see 759. Find under "Induction" at Commens Dictionary of Peirce's Terms.
88. ^ . Brown, C. (2005) Overcoming Barriers to Use of Promising Research Among Elite Middle East Policy Groups, Journal of Social Behaviour and Personality, Select Press.
89. ^ Hanson, Norwood (1958), Patterns of Discovery, Cambridge University Press, ISBN 0-521-05197-5 
90. ^ Kuhn 1962, p. 113 ISBN 978-1443255448
91. ^ Feyerabend, Paul K (1960) "Patterns of Discovery" The Philosophical Review (1960) vol. 69 (2) pp. 247-252
92. ^ Kuhn, Thomas S., "The Function of Measurement in Modern Physical Science", ISIS 52(2), 161–193, 1961.
93. ^ Feyerabend, Paul K., Against Method, Outline of an Anarchistic Theory of Knowledge, 1st published, 1975. Reprinted, Verso, London, UK, 1978.
94. ^
    • Higher Superstition: The Academic Left and Its Quarrels with Science, The Johns Hopkins University Press, 1997
    • Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science, Picador; 1st Picador USA Pbk. Ed edition, 1999
    • The Sokal Hoax: The Sham That Shook the Academy, University of Nebraska Press, 2000 ISBN 0-8032-7995-7
    • A House Built on Sand: Exposing Postmodernist Myths About Science, Oxford University Press, 2000
    • Intellectual Impostures, Economist Books, 2003
95. ^ ^{a b c} Dunbar, K., & Fugelsang, J. (2005). Causal thinking in science: How scientists and students interpret the unexpected. In M. E. Gorman, R. D. Tweney, D. Gooding & A. Kincannon (Eds.), Scientific and Technical Thinking (pp. 57-79). Mahwah, NJ: Lawrence Erlbaum Associates.
96. ^ ^{a b} Oliver, J.E. (1991) Ch2. of The incomplete guide to the art of discovery. New York:NY, Columbia University Press.
97. ^ Talib contributes a brief description of anti-fragility, http://www.edge.org/q2011/q11_3.html
98. ^ Riccardo Pozzo (2004) The impact of Aristotelianism on modern philosophy. CUA Press. p.41. ISBN 0813213479
99. ^ The ancient Egyptians observed that heliacal rising of a certain star, Sothis (Greek for Sopdet (Egyptian), known to the West as Sirius), marked the annual flooding of the Nile river. See Neugebauer, Otto (1969) [1957], The Exact Sciences in Antiquity (2 ed.), Dover Publications, ISBN 978-048622332-2, http://books.google.com/?id=JVhTtVA2zr8C , p.82, and also the 1911 Britannica, "Egypt".
100. ^ The Rhind papyrus lists practical examples in arithmetic and geometry —1911 Britannica, "Egypt".
101. ^ The Ebers papyrus lists some of the 'mysteries of the physician', as cited in the 1911 Britannica, "Egypt"
102. ^ Rosanna Gorini (2003), "Al-Haytham the Man of Experience, First Steps in the Science of Vision", International Society for the History of Islamic Medicine, Institute of Neurosciences, Laboratory of Psychobiology and Psychopharmacology, Rome, Italy:

     "According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable."

103. ^ Bacon, Francis Novum Organum (The New Organon), 1620. Bacon's work described many of the accepted principles, underscoring the importance of theory, empirical results, data gathering, experiment, and independent corroboration.
104. ^ "John Stuart Mill (Stanford Encyclopedia of Philosophy)". plato.stanford.edu. http://plato.stanford.edu/entries/mill/#SciMet. Retrieved 2009-07-31. 
105. ^ Gauch 2003, pp. 52–53
106. ^ George Sampson (1970). The concise Cambridge history of English literature. Cambridge University Press. p.174. ISBN 0521095816
107. ^ Logik der Forschung, new appendices *XVII–*XIX (not yet available in the English edition Logic of scientific discovery)
108. ^ Logic of Scientific discovery, p. 20
109. ^ ^{a b} Karl Popper: On the non-existence of scientific method. Realism and the Aim of Science (1983)
110. ^ Karl Popper: Science: Conjectures and Refutations. Conjectures and Refuations, section VII
111. ^ Karl Popper: On knowledge. In search of a better world, section II
112. ^ "When we are working intensively, we feel keenly the progress of our work; we are elated when our progress is rapid, we are depressed when it is slow." — the mathematician Pólya 1957, p. 131 in the section on 'Modern heuristic'.
113. ^ "Philosophy [i.e., physics] is written in this grand book--I mean the universe--which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth." —Galileo Galilei, Il Saggiatore (The Assayer, 1623), as translated by Stillman Drake (1957), Discoveries and Opinions of Galileo pp. 237-8, as quoted by di Francia 1981, p. 10.
114. ^ Pólya 1957 2nd ed.
115. ^ George Pólya (1954), Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics,
116. ^ George Pólya (1954), Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning.
117. ^ Pólya 1957, p. 142
118. ^ Pólya 1957, p. 144
119. ^ Mackay 1991 p.100
120. ^ See the development, by generations of mathematicians, of Euler's formula for polyhedra as documented by Lakatos, Imre (1976), Proofs and refutations, Cambridge: Cambridge University Press, ISBN 0-521-29038-4 

References

• Born, Max (1949), Natural Philosophy of Cause and Chance, Peter Smith , also published by Dover, 1964. From the Waynflete Lectures, 1948. On the web. N.B.: the web version does not have the 3 addenda by Born, 1950, 1964, in which he notes that all knowledge is subjective. Born then proposes a solution in Appendix 3 (1964)
• Brody, Thomas A. (1993), The Philosophy Behind Physics, Springer Verlag, ISBN 0-387-55914-0 . (Luis De La Peña and Peter E. Hodgson, eds.)
• Bruno, Leonard C. (1989), The Landmarks of Science, ISBN 0-8160-2137-6 
• Bynum, W.F.; Porter, Roy (2005), Oxford Dictionary of Scientific Quotations, Oxford, ISBN 0-19-858409-1 .
• di Francia, G. Toraldo (1981), The Investigation of the Physical World, Cambridge University Press, ISBN 0-521-29925-X .
• Einstein, Albert; Infeld, Leopold (1938), The Evolution of Physics: from early concepts to relativity and quanta, New York: Simon and Schuster, ISBN 0-671-20156-5 
• Feynman, Richard (1965), The Character of Physical Law, Cambridge: M.I.T. Press, ISBN 0-262-56003-8 .
• Fleck, Ludwik (1979), Genesis and Development of a Scientific Fact, Univ. of Chicago, ISBN 0-226-25325-2 . (written in German, 1935, Entstehung und Entwickelung einer wissenschaftlichen Tatsache: Einführung in die Lehre vom Denkstil und Denkkollectiv) English translation, 1979
• Galileo (1638), Two New Sciences, Leiden: Lodewijk Elzevir, ISBN 0-486-60099-8  Translated from Italian to English in 1914 by Henry Crew and Alfonso de Salvio. Introduction by Antonio Favaro. xxv+300 pages, index. New York: Macmillan, with later reprintings by Dover.
• Gauch, Hugh G., Jr. (2003), Scientific Method in Practice, Cambridge University Press, ISBN 0-521-01708-4, http://books.google.com/?id=iVkugqNG9dAC  435 pages
• Glen, William (ed.) (1994), The Mass-Extinction Debates: How Science Works in a Crisis, Stanford, CA: Stanford University Press, ISBN 0-8047-2285-4 .
• Godfrey-Smith, Peter (2003), Theory and Reality: An introduction to the philosophy of science, University of Chicago Press, ISBN 0-226-30063-3 .
• Goldhaber, Alfred Scharff; Nieto, Michael Martin (January–March 2010), "Photon and graviton mass limits", Rev. Mod. Phys. (American Physical Society) 82: 939, doi:10.1103/RevModPhys.82.939 . pages 939-979.
• Jevons, William Stanley (1874), The Principles of Science: A Treatise on Logic and Scientific Method, Dover Publications, ISBN 1430487755 . 1877, 1879. Reprinted with a foreword by Ernst Nagel, New York, NY, 1958.
• Kuhn, Thomas S. (1962), The Structure of Scientific Revolutions, Chicago, IL: University of Chicago Press . 2nd edition 1970. 3rd edition 1996.
• Mackay, Alan L. (ed.) (1991), Dictionary of Scientific Quotations, London: IOP Publishing Ltd, ISBN 0-7503-0106-6 
• McElheny, Victor K. (2004), Watson & DNA: Making a scientific revolution, Basic Books, ISBN 0-7382-0866-3 .
• Moulton, Forest Ray; Schifferes, Justus J. (eds., Second Edition) (1960), The Autobiography of Science, Doubleday .
• Needham, Joseph; Wang, Ling (王玲) (1954), Science and Civilisation in China, 1 Introductory Orientations, Cambridge University Press 
• Newton, Isaac (1687, 1713, 1726), Philosophiae Naturalis Principia Mathematica, University of California Press, ISBN 0-520-08817-4 , Third edition. From I. Bernard Cohen and Anne Whitman's 1999 translation, 974 pages.
• Ørsted, Hans Christian (1997), Selected Scientific Works of Hans Christian Ørsted, Princeton, ISBN 0-691-04334-5 . Translated to English by Karen Jelved, Andrew D. Jackson, and Ole Knudsen, (translators 1997).
• Peirce, C. S. — see Charles Sanders Peirce bibliography.
• Poincaré, Henri (1905), Science and Hypothesis  Eprint
• Pólya, George (1957), How to Solve It, Princeton University Press, ISBN -691-08097-6 
• Popper, Karl R., The Logic of Scientific Discovery, 1934, 1959.
• Sambursky, Shmuel (ed.) (1974), Physical Thought from the Presocratics to the Quantum Physicists, Pica Press, ISBN 0-87663-712-8 .
• Taleb, Nassim Nicholas (2007), The Black Swan, Random House, ISBN 978-1-4000-6351-2 
• Watson, James D. (1968), The Double Helix, New York: Atheneum, Library of Congress card number 68-16217 .

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., The Art of Scientific Investigation, Heinemann, Melbourne, Australia, 1950.
• Bernstein, Richard J., 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. What is this thing called science?. Queensland University Press and Open University Press, 1976.
• Crick, Francis (1988), What Mad Pursuit: A Personal View of Scientific Discovery, New York: Basic Books, ISBN 0-465-09137-7 .
• Dewey, John, How We Think, D.C. Heath, Lexington, MA, 1910. Reprinted, Prometheus Books, Buffalo, NY, 1991.
• Earman, John (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, The Scientific Image, Oxford University Press, Oxford, UK, 1980.
• Franklin, James (2009), What Science Knows: And How It Knows It, New York: Encounter Books, ISBN 1594032076 .
• Gadamer, Hans-Georg, 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, Representing and Intervening, Introductory Topics in the Philosophy of Natural Science, Cambridge University Press, Cambridge, UK, 1983.
• Heisenberg, Werner, Physics and Beyond, Encounters and Conversations, A.J. Pomerans (trans.), Harper and Row, New York, NY 1971, pp. 63–64.
• Holton, Gerald, 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, 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, The Comprehensibility of the Universe: A New Conception of Science, Oxford University Press, Oxford, 1998. Paperback 2003.
• McCarty, Maclyn (1985), The Transforming Principle: Discovering that genes are made of DNA, New York: W. W. Norton, pp. 252  , ISBN 0-393-30450-7 . Memoir of a researcher in the Avery–MacLeod–McCarty experiment.
• McComas, William F., ed. The Principal Elements of the Nature of Science: Dispelling the MythsPDF (189 KB), 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, Renewing Philosophy, Harvard University Press, Cambridge, MA, 1992.
• Rorty, Richard, Philosophy and the Mirror of Nature, Princeton University Press, Princeton, NJ, 1979.
• Salmon, Wesley C., Four Decades of Scientific Explanation, University of Minnesota Press, Minneapolis, MN, 1990.
• Shimony, Abner, 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 (2000). Real Science: what it is, and what it means. Cambridge, UK: Cambridge University Press.

External links

• An Introduction to Science: Scientific Thinking and a scientific method by Steven D. Schafersman.
• Introduction to a scientific method
• Theory-ladenness by Paul Newall at The Galilean Library
• Lecture on Scientific Method by Greg Anderson
• Using the scientific method for designing science fair projects
• SCIENTIFIC METHODS an online book by Richard D. Jarrard
• Richard Feynman on the Key to Science (one minute, three seconds), from the Cornell Lectures.