Dichotomy describes a structure of two parts that face each other without any intersection . They can complement each other, for example a complementary pair of terms, or express a division into two parts, for example the division of an area into two parts.
Dichotomy literally means 'to cut in half , to cut up' ( ancient Greek διχοτομία dichotomía ; from ancient Greek δίχα dícha , German 'in two' , 'separated' and ancient Greek τέμνειν témnein , German 'cut' ). The adjective is dichotomous or dichotomous. One speaks, for example, of a dichotomous or dichotomous method if it is based on a division into two parts or groups.
Dichotomy in the sense of set theory
The decisive factor in the dichotomous division of a set (example: division into two terms A and B) is that
- each element is to be assigned to one or the other subset (A or B) and
- no element can be assigned to both subsets (terms) at the same time; the subsets must not have any intersection (the terms are disjoint ).
In the case of a dichotomous division, the error of inadequate division is excluded. It is required that two complementary terms fully encompass the scope or meaning of the original term. An incomplete classification or an overlapping classification is therefore not possible. The union of the dichotomous concepts leads back to the original concept.
Dichotomous classifications are not always practical. For example, in the case of a striking division of the population into old and young, city and country, black and white (skin color), the differences can be overemphasized and possible similarities are lost from view (“black and white painting”).
Dichotomies in Mathematics
Examples from the fields of mathematics and logic:
- the division of whole numbers into even and odd numbers,
- the division of real numbers into rational and irrational numbers ,
- the division of the rational numbers into whole numbers and fractions, the numerators and denominators of which are relatively prime ,
- the division of statements into true and false statements.
In statistics , a dichotomous or binary variable is understood to be a variable that has two characteristics, for example the variable “coin” with the two characteristics “heads” and “tails”.
In test theory , an answer format is called dichotomous if only two answer options are given, for example “yes” and “no”. In contrast to this, answer formats with multiple levels are also used, for example “never”, “rarely”, “sometimes”, “often” and “always”.
In mathematical optimization , a dichotomous process is understood to be a method of local non-linear optimization without secondary conditions. One such method that works with halving intervals of equal size is the interval halving method .
Dichotomies in Astronomy
In astronomy , the phase during which a star that does not shine itself - usually a planet or moon as opposed to a star - is seen by an observer to be half-lit is called a dichotomy. In visual astronomy , dichotomy therefore also means “ half-phase ”: A planet or moon is illuminated precisely from the side (i.e. at a phase angle of 90 °) so that it appears as a semicircle . The best known example is the phase of the crescent moon , from which, for example, Aristarchus of Samos was able to estimate the distance of the moon. From earth, half-phases can only be observed in the lower planets Mercury and Venus , except for the moon .
In planetology , the term stands for the appearance of two conspicuously differently shaped hemispheres, which is common among the solid celestial bodies. The best-known examples are, besides the earth and the earth's moon, the planet Mars and the Saturn moon Iapetus :
- in the case of the earth, the striking difference between land and water hemisphere - a consequence of the formation of the Pacific ,
- on the moon, the many mars on the front, which are largely missing on the back of the moon - a consequence of the " Great Bombardment " by asteroids about four billion years ago,
- Mars has a similar “dichotomy” between the northern and southern hemisphere : in the north mainly lowlands , in the south huge highlands . (The central great circle that separates these topographical hemispheres is inclined 40 ° to the equator . The asymmetrical mass distribution means that the center of gravity of Mars is offset from the geometric center by three kilometers in the direction of the northern lowlands.)
The term “ Venus dichotomy” is not used correctly because it does not apply to the half-phase, but to the temporary sickle shape of the evening or morning star. The "horns" of the Venus sickle are not facing each other by 180 °, but overlap, a result of the dense Venusian atmosphere. This “dichotomy” of the Venus sickle was noticed as early as the 17th century, can also be observed in daytime observations and was a way of estimating the density of the atmosphere before the space travel era . Because it turned out to be astonishingly tight, the assumption arose from Hieronymus Schröter that there might be Venusians .
Dichotomy in clinical psychology
In clinical psychology dichotomy stands for an absolute thought pattern and a cognitive bias , in which a person is only divided into two extreme levels or categories and ignored that there is a scale of gray levels in between. That is why we speak of “all-or-nothing thinking” . When thinking in black and white, the patient shifts neutral (gray) information into the negative (black) category, which indicates depressive thinking. Dichotomy can be a cognitive bias of depression and other mental illnesses such as borderline personality disorder and dissociative identity disorder . For example, in dissociative identity disorder, a child who has been molested by the father creates a partial personality who loves the father and one who hates him. The reason for this is that the deed cannot coexist with the love of the father and so two contrary personalities are created who know nothing of each other or do not want to exchange ideas.
Examples of dichotomous thinking are e.g. B. the division into good and bad, the division into flawless and faulty, the division into clean and dirty, or the division into holy and sinful. Dichotomous thinking can also be used with prejudices and role models, such as B. the division into female and male behavior.
People mostly use dichotomous thinking in order to condense and contrast intellectual considerations so that there is little doubt about the action and this can therefore be carried out consistently. It is also used to arrive at a relatively clear decision-making process despite multi-layered and complex conflicts and to reduce the complexity of decision-making and thereby save cognitive processes and time. In a social context, people are usually concerned with differentiating themselves from others with their position and asserting themselves, which can lead to dichotomous thinking.
However, many options for weighing up are lost in this way of thinking and the facts are assessed too quickly, one-sidedly and subjectively, so that there is often a lack of balanced discourse and dialogue or it is avoided. In groups and organizations, the rhetorical strategy advocatus diaboli can therefore also be used to criticize the current state of the discussion and thus to question limitations and one-sidedness and to correct them accordingly.
Dichotomies in other areas
In phylogenetics , branches of evolutionary branches are assumed to be dichotomous and, if relationships are unclear, they are described as polytomous nodes in cladograms or family trees.
In German criminal law , the division of offenses into crimes and offenses in accordance with Criminal Code is referred to as the “dichotomy of criminal law”, which with the reforms of 1974 and 1975 replaced the trichotomy (three-part division) that previously existed in Germany based on the French model .
The should -be dichotomy is a metaethical principle according to which there is a dichotomous division into descriptive and normative statements in ethics. That is why one cannot infer an ought to be from a being .
In philosophy , there are several lessons to return the structure of reality on two principles. One example is hylemorphism . This is the modern term for a central teaching in the philosophy of Aristotle , according to which finite substances consist of two different principles, namely the substance or matter (Greek hýlē) and the form (Greek morphḗ).
- Dihairesis (see there theory of Dihairesis )
- False dilemma ("false dichotomy")
- Polytomy (multiple division)
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