Scientific method

The scientific method seeks to explain the events of nature in a reproducible way, and to use these reproductions to make useful predictions. It is done through observation of natural phenomena, and/or through experimentation that tries to simulate natural events under controlled conditions. It provides an objective process to find solutions to problems in a number of scientific and technological fields.

Based on observations of a phenomenon, a scientist may generate a model. This is an attempt to describe or depict the phenomenon in terms of a logical physical or mathematical representation. As empirical evidence is gathered, a scientist can suggest a hypothesis to explain the phenomenon. This description can be used to make predictions that are testable by experiment or observation using the scientific method. When a hypothesis proves unsatisfactory, it is either modified or discarded.

While performing experiments, Scientists may have a preference for one outcome over another, and it is important that this tendency does not bias their interpretation.[7][8] A strict following of the scientific method attempts to minimize the influence of a scientist's bias on the outcome of an experiment. This can be achieved by correct experimental design, and a thorough peer review of the experimental results as well as conclusions of a study.[9][10] Once the experiment results are announced or published, an important cross-check can be the need to validate the results by an independent party.

Once a hypothesis has survived testing, it may become adopted into the framework of a scientific theory. This is a logically reasoned, self-consistent model or framework for describing the behavior of certain natural phenomena. A theory typically describes the behavior of much broader sets of phenomena than a hypothesis—commonly, a large number of hypotheses can be logically bound together by a single theory. These broader theories may be formulated using principles such as parsimony (e.g., "Occam's Razor"). They are then repeatedly tested by analyzing how the collected evidence (facts) compares to the theory. When a theory survives a sufficiently large number of empirical observations, it then becomes a scientific generalization that can be taken as fully verified. These assume the status of a physical law or law of nature.

Despite the existence of well-tested theories, science cannot claim absolute knowledge of nature or the behavior of the subject or of the field of study due to epistemological problems that are unavoidable and preclude the discovery or establishment of absolute truth. Unlike a mathematical proof, a scientific theory is empirical, and is always open to falsification, if new evidence is presented. Even the most basic and fundamental theories may turn out to be imperfect if new observations are inconsistent with them. Critical to this process is making every relevant aspect of research publicly available, which allows ongoing review and repeating of experiments and observations by multiple researchers operating independently of one another. Only by fulfilling these expectations can it be determined how reliable the experimental results are for potential use by others.

Isaac Newton's Newtonian law of gravitation is a famous example of an established law that was later found not to be universal—it does not hold in experiments involving motion at speeds close to the speed of light or in close proximity of strong gravitational fields. Outside these conditions, Newton's Laws remain an excellent model of motion and gravity. Since general relativity accounts for all the same phenomena that Newton's Laws do and more, general relativity is now regarded as a more comprehensive theory.

Mathematics
Data from the famous Michelson–Morley experiment
Data from the famous Michelson–Morley experiment

Mathematics is essential to many sciences. One important function of mathematics in science is the role it plays in the expression of scientific models. Observing and collecting measurements, as well as hypothesizing and predicting, often require extensive use of mathematics and mathematical models. Calculus may be the branch of mathematics most often used in science[citation needed], but virtually every branch of mathematics has applications in science, including "pure" areas such as number theory and topology. Mathematics is fundamental to the understanding of the natural sciences and the social sciences, many of which also rely heavily on statistics.

Statistical methods, comprised of mathematical techniques for summarizing and exploring data, allow scientists to assess the level of reliability and the range of variation in experimental results. Statistical thinking also plays a fundamental role in many areas of science.

Computational science applies computing power to simulate real-world situations, enabling a better understanding of scientific problems than formal mathematics alone can achieve. According to the Society for Industrial and Applied Mathematics, computation is now as important as theory and experiment in advancing scientific knowledge.

Whether mathematics itself is properly classified as science has been a matter of some debate. Some thinkers see mathematicians as scientists, regarding physical experiments as inessential or mathematical proofs as equivalent to experiments. Others do not see mathematics as a science, since it does not require experimental test of its theories and hypotheses. In practice, mathematical theorems and formulas are obtained by logical derivations which presume axiomatic systems, rather than a combination of empirical observation and method of reasoning that has come to be known as scientific method. In general, mathematics is classified as formal science, while natural and social sciences are classified as empirical sciences.

http://en.wikipedia.org/wiki/Science#History_of_science