Analysis

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Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.[1]

The word comes from the Ancient Greek ἀνάλυσις (analusis, "a breaking up", from ana- "up, throughout" and lysis "a loosening").[2]

As a formal concept, the method has variously been ascribed to Alhazen,[3] René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).

Applicants[edit]

Chemistry[edit]

The field of chemistry uses analysis in at least three ways: to identify the components of a particular chemical compound (qualitative analysis), to identify the proportions of components in a mixture (quantitative analysis), and to break down chemical processes and examine chemical reactions between elements of matter. For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze neutron activation to develop discrete measurements within vast samples. A matrix can have a considerable effect on the way a chemical analysis is conducted and the quality of its results. Analysis can be done manually or with a device. Chemical analysis is an important element of national security among the major world powers with materials measurement and signature intelligence (MASINT) capabilities.

Isotopes[edit]

Chemists can use isotope analysis to assist analysts with issues in anthropology, archeology, food chemistry, forensics, geology, and a host of other questions of physical science. Analysts can discern the origins of natural and man-made isotopes in the study of environmental radioactivity.

Business[edit]

Computer science[edit]

Economics[edit]

Engineering[edit]

Analysts in the field of engineering look at requirements, structures, mechanisms, systems and dimensions. Electrical engineers analyse systems in electronics. Life cycles and system failures are broken down and studied by engineers. It is also looking at different factors incorporated within the design.

Intelligence[edit]

The field of intelligence employs analysts to break down and understand a wide array of questions. Intelligence agencies may use heuristics, inductive and deductive reasoning, social network analysis, dynamic network analysis, link analysis, and brainstorming to sort through problems they face. Military intelligence may explore issues through the use of game theory, Red Teaming, and wargaming. Signals intelligence applies cryptanalysis and frequency analysis to break codes and ciphers. Business intelligence applies theories of competitive intelligence analysis and competitor analysis to resolve questions in the marketplace. Law enforcement intelligence applies a number of theories in crime analysis.

Linguistics[edit]

Linguistics began with the analysis of Sanskrit and Tamil; today it looks at individual languages and language in general. It breaks language down and analyses its component parts: theory, sounds and their meaning, utterance usage, word origins, the history of words, the meaning of words and word combinations, sentence construction, basic construction beyond the sentence level, stylistics, and conversation. It examines the above using statistics and modeling, and semantics. It analyses language in context of anthropology, biology, evolution, geography, history, neurology, psychology, and sociology. It also takes the applied approach, looking at individual language development and clinical issues.

Literature[edit]

Literary theory is the analysis of literature. Some say that literary criticism is a subset of literary theory. The focus can be as diverse as the analysis of Homer or Freud. This is mainly to do with the breaking up of a topic to make it easier to understand.

Mathematics[edit]

Modern mathematical analysis is the study of infinite processes. It is the branch of mathematics that includes calculus. It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors.

Florian Cajori explains in A History of Mathematics (1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows:

The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in [appended to] Euclid, XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."

The analytic method is not conclusive, unless all operations involved in it are known to be reversible. To remove all doubt, the Greeks, as a rule, added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions.

James Gow uses a similar argument as Cajori, with the following clarification, in his A Short History of Greek Mathematics (1884):

The synthetic proof proceeds by shewing that the proposed new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is founded. The Greeks distinguished theoretic from problematic analysis. A theoretic analysis is of the following kind. To prove that A is B, assume first that A is B. If so, then, since B is C and C is D and D is E, therefore A is E. If this be known a falsity, A is not B. But if this be a known truth and all the intermediate propositions be convertible, then the reverse process, A is E, E is D, D is C, C is B, therefore A is B, constitutes a synthetic proof of the original theorem. Problematic analysis is applied in all cases where it is proposed to construct a figure which is assumed to satisfy a given condition. The problem is then converted into some theorem which is involved in the condition and which is proved synthetically, and the steps of this synthetic proof taken backwards are a synthetic solution of the problem.

Music[edit]

Philosophy[edit]

Psychotherapy[edit]

Signal processing[edit]

Statistics[edit]

In statistics, the term analysis may refer to any method used for data analysis. Among the many such methods, some are:

  • Analysis of variance (ANOVA) – a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts
  • Boolean analysis – a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis
  • Cluster analysis – techniques for grouping objects into a collection of groups (called clusters), based on some measure of proximity or similarity
  • Factor analysis – a method to construct models describing a data set of observed variables in terms of a smaller set of unobserved variables (called factors)
  • Meta-analysis – combines the results of several studies that address a set of related research hypotheses
  • Multivariate analysis – analysis of data involving several variables, such as by factor analysis, regression analysis, or principal component analysis
  • Principal component analysis – transformation of a sample of correlated variables into uncorrelated variables (called principal components), mostly used in exploratory data analysis
  • Regression analysis – techniques for analyzing the relationships between several variables in the data
  • Scale analysis (statistics) – methods to analyze survey data by scoring responses on a numeric scale
  • Sensitivity analysis – the study of how the variation in the output of a model depends on variations in the inputs
  • Sequential analysis – evaluation of sampled data as it is collected, until the criterion of a stopping rule is met
  • Spatial analysis – the study of entities using geometric or geographic properties
  • Time-series analysis – methods that attempt to understand a sequence of data points spaced apart at uniform time intervals

Other[edit]

  • Aura analysis – a technique in which supporters of the method claim that the body's aura, or energy field is analysed
  • Bowling analysis – Analysis of the performance of cricket players
  • Lithic analysis – the analysis of stone tools using basic scientific techniques
  • Protocol analysis – a means for extracting persons' thoughts while they are performing a task

See also[edit]

References[edit]

  1. ^ Michael Beaney (Summer 2012). "Analysis". The Stanford Encyclopedia of Philosophy. Michael Beaney. Retrieved 23 May 2012. 
  2. ^ Douglas Harper (2001–2012). "analysis (n.)". ONLINE ETYMOLOGY DICTIONARY. Douglas Harper. Retrieved 23 May 2012. 
  3. ^ O'Connor, John J.; Robertson, Edmund F., "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, University of St Andrews .

External links[edit]