Instruct: Given a question, retrieve relevant passages that answer the question.
Query: What is the first step in the dialectical method?
Within Hegelianism, the word dialectic has the specialised meaning of a contradiction between ideas that serves as the determining factor in their relationship. Dialectic comprises three stages of development: first, a thesis or statement of an idea, which gives rise to a second step, a reaction or antithesis that contradicts or negates the thesis, and third, the synthesis, a statement through which the differences between the two points are resolved. Dialectical materialism, a theory or set of theories produced mainly by Karl Marx and Friedrich Engels, adapted the Hegelian dialectic into arguments regarding traditional materialism.
The FOIL method is equivalent to a two-step process involving the distributive law:
In the first step, the () is distributed over the addition in first binomial. In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributive can be applied easily to products with more terms such as trinomials and higher.
Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. The process continues with subsequent steps to map out the solution. Single-step methods (such as Euler's method) refer to only one previous point and its derivative to determine the current value. Methods such as Runge–Kutta take some intermediate steps (for example, a half-step) to obtain a higher order method, but then discard all previous information before taking a second step. Multistep methods attempt to gain efficiency by keeping and using the information from previous steps rather than discarding it. Consequently, multistep methods refer to several previous points and derivative values. In the case of "linear" multistep methods, a linear combination of the previous points and derivative values is used.
Popper believed that Marxism had been initially scientific, in that Marx had postulated a theory which was genuinely predictive. When Marx's predictions were not in fact borne out, Popper argues that the theory was saved from falsification by the addition of "ad hoc" hypotheses which attempted to make it compatible with the facts. By this means, a theory which was initially genuinely scientific degenerated into pseudoscientific dogma. Popper agreed on the general non-falsifiability of the social sciences, but instead used it as an argument against central planning and all-encompassing historiographical ideologies. Popper devoted much attention to dissecting the practice of using the dialectic in defence of Marxist thought, which was the very strategy employed by V.A. Lektorsky in his defence of Marxism against Popper's criticisms. Among Popper's conclusions was that Marxists used dialectic as a method of side-stepping and evading criticisms, rather than actually answering or addressing them: Hegel thought that philosophy develops; yet his own system was to remain the last and highest stage of this development and could not be superseded. The Marxists adopted the same attitude towards the Marxian system. Hence, Marx's anti-dogmatic attitude exists only in the theory and not in the practice of orthodox Marxism, and dialectic is used by Marxists, following the example of Engels' Anti-Dühring, mainly for the purposes of apologetics – to defend the Marxist system against criticism. As a rule critics are denounced for their failure to understand the dialectic, or proletarian science, or for being traitors. Thanks to dialectic the anti-dogmatic attitude has disappeared, and Marxism has established itself as a dogmatism which is elastic enough, by using its dialectic method, to evade any further attack. It has thus become what I have called reinforced dogmatism.
The earlier dialogues of Plato (424–348 BCE), relating the debates of his teacher Socrates, raised the use of arguments to a formal dialectical method (), now called the Socratic method which is taught in law schools. Typically Socrates' opponent would make an innocuous assertion, then Socrates by a step-by-step train of reasoning, bringing in other background assumptions, would make the person admit that the assertion resulted in an absurd or contradictory conclusion, forcing him to abandon his assertion. The technique was also a focus of the work of Aristotle (384–322 BCE).
Clustal Omega has five main steps in order to generate the multiple sequence alignment. The first is producing a pairwise alignment using the k-tuple method, also known as the word method. This, in summary, is a heuristic method that isn't guaranteed to find an optimal alignment solution, but is significantly more efficient than the dynamic programming method of alignment. After that, the sequences are clustered using the modified mBed method. The mBed method calculates pairwise distance using sequence embedding. This step is followed by the k-means clustering method. Next, the guide tree is constructed using the UPGMA method. This is shown as multiple guide tree steps leading into one final guide tree construction because of the way the UPGMA algorithm works. At each step, (each diamond in the flowchart) the nearest two clusters are combined and is repeated until the final tree can be assessed. In the final step, the multiple sequence alignment is produced using HHAlign package from the HH-Suite, which uses two profile HMM's. A profile HMM is a linear state machine consisting of a series of nodes, each of which corresponds roughly to a position (column) in the alignment from which it was built. 
The first step is understanding a patient's symptoms and how they behave. Such as where patient feels pain and when, how often in a day, to what degree, and in what specific movements or positions does pain intensify or express itself. The patient will be tested and asked by a clinician to perform specific single direction movement, both sustained and repeated. A large differentiator from other physical therapy methods of assessment is the use of repeated movements. A range of single direction movements are used in this phase of the McKenzie method, depending on how pain symptoms behave and change will allow the clinician to categorise the problem to effectively prescribe the proper movements to achieve centralisation and elimination of spinal and sciatic pain.
Quick Steps Tempo - 112-124 beats to the minute
Thirteenth Step: Shedding with Back-Step
Fourteenth Step: Toe-and-Heel and Rock
Fifteenth Step: Pointing and Back-Stepping
Sixteenth Step: Heel-and-Toe and Shedding
Seventeenth Step: Heel-and-Toe, Shedding, and Back-Stepping
Eighteenth Step: Back-Stepping
Finish Method 1: One Leap
Finish Method 2: Two Leaps 
Finish Method 3: Two Highland Fling turns
Entrechat Endings: 
Method 1: One Entrechat
Method 2: 2 Entrechats
Method 3: Leap then Entrechat 
Method 4: Entrechat then Leap
Method 5: Leap, Entrechat, Leap
Method 6: Leap, Entrechat, Leap, Entrechat
Trust-region methods are in some sense dual to line-search methods: trust-region methods first choose a step size (the size of the trust region) and then a step direction, while line-search methods first choose a step direction and then a step size.
Critique of Dialectical Reason () is a 1960 book by the philosopher Jean-Paul Sartre, in which the author further develops the existentialist Marxism he first expounded in his essay "Search for a Method" (1957). "Critique of Dialectical Reason" and "Search for a Method" were written as a common manuscript, with Sartre intending the former to logically precede the latter. "Critique of Dialectical Reason" was Sartre's second large-scale philosophical treatise, "Being and Nothingness" (1943) having been the first. The book has been seen by some as an abandonment of Sartre's original existentialism, while others have seen it as a continuation and elaboration of his earlier work. It was translated into English by Alan Sheridan-Smith.
According to Gewirth's theory, the PGC, is derivable from the fact of human agency, but it is derivable only via a "dialectically necessary" mode of argumentation. The mode is "dialectical" in the sense that it presents the steps of the argument to the PGC as inferences made by an agent, rather than as statements true of the world itself. Each step is thus a description of what the agent thinks (or implicitly asserts), not what things are like independently of the viewpoint of the agent. This mode of argumentation is also "necessary" both in the sense that its initial premise is inescapable from any agent's standpoint and that the subsequent steps of the proof are logically deduced from this premise.
The CFOP (Cross - F2L - OLL - PLL) method, also known as the Fridrich Method, was named after one of its inventors, Jessica Fridrich, who finished second in the 2003 Rubik's Cube World Championships. While it is known as the Fridrich method, its origins are actually credited to David Singmaster, who was one of the first to publish a layer by layer method of solving in 1980, and Guus Razoux Schultz, who built upon this and developed a more efficient system for the first two layers (F2L). Jessica Fridrich then finished developing the method and published it online in 1997, an event that was very influential in the revival of competitive speedcubing. The first step of the method is to solve a cross-shaped arrangement of edge pieces on the first layer. The remainder of the first layer and all of the second layer are then solved together in what are referred to as "corner-edge pairs", or slots. Finally, the last layer is solved in two steps — first, all of the pieces in the layer are oriented to form a solid color (but without the individual pieces always being in their correct places on the cube). This step is referred to as orientation and is usually performed with a single set of algorithms known as OLL (Orientation of Last Layer). Then, all of those pieces are permuted to their correct spots. This is also usually performed as a single set of algorithms known as PLL (Permutation of Last Layer).
The CFOP Method can be used as a less-advanced method by dividing the steps into more steps, reducing the number of algorithms you need to learn but sacrifices time. Most people start learning CFOP with 4LLL (Four-Look Last Layer), which is the less advanced, slower, and algorithm-reducing way to learn CFOP. The 4 steps are divided into Edge Orientation, Corner Orientation, Corner Permutation, and Edge Permutation. Later on, you can learn Full PLL which replaces the permutation of the edges and corners, making the solve more efficient and therefore faster. Even later, you can learn Full OLL which will replace the Orientation of the corners and edges, again making the solve faster.
The basic approach for building the stock correlation network involves two steps. The first step aims at finding the correlation between each pair of stock considering their corresponding time series. The second step applies a criterion to connect the stocks based on their correlation. The popular method for connecting two correlated stocks is the minimum spanning tree method. The other methods are, planar maximally filtered graph, and winner take all method. In all three methods, the procedure for finding correlation between stocks remains the same.
Johannes Schmidt used a second metaphor to explain the formation of a language from a continuum. The continuum is at first like a smooth, sloping line. Speakers in close proximity tend to unify their speech, creating a stepped line out of the sloped line. These steps are the dialects. Over the course of time, some steps become weak and fall into disuse, while others preempt the entire continuum. As example Schmidt used Standard German, which was defined to conform to some dialects and then spread throughout Germany, replacing the local dialects in many cases.
A pioneering study in traditional perceptual dialectology took place in the Netherlands in 1939 and was conducted by W.G. Rensink. The study sought to investigate perceptual dialect boundaries through a Dutch dialect survey in which subjects were asked to state whether they thought other people spoke the same or different dialect as them, and what the dialect difference was if there was deemed to be any. Weijnen analyzed this data through the little-arrow method that she devised. Many studies proceeded from this, and perceptual dialectology surveys took place in various countries.
The MacCormack method is a variation of the two-step Lax–Wendroff scheme but is much simpler in application. To illustrate the algorithm, consider the following first order hyperbolic equation
The application of MacCormack method to the above equation proceeds in two steps; a "predictor step" which is followed by a "corrector step". 
Hargreaves and colleagues offer a series of five questions that researchers should answer to decide whether SWT is indeed the optimal design, and how to proceed in every step of the study. Specifically, researchers should be able to identify:While there are several other potential methods for modeling outcomes in an SWT, the work of Hussey and Hughes "first described methods to determine statistical power available when using a stepped wedge design." What follows is their design.
Georg Wilhelm Friedrich Hegel (1770–1831) is the philosopher who brought the dialectical method to a new pinnacle of development. According to Hegel in "Science of Logic", the dialectical methods consists of three steps. First, a thesis is given, which can be any proposition in logic. Second, the antithesis of the thesis is formed and, finally, a synthesis incorporating both thesis and antithesis. Hegel believed that no proposition taken by itself can be completely true. Only the whole can be true, and the dialectical synthesis was the means by which the whole could be examined in relation to a specific proposition. Truth consists of the whole process. Separating out thesis, antithesis, or synthesis as a stand-alone statement results in something that is in some way or other untrue. The concept of "nothing" arises in Hegel right at the beginning of his "Logic". The whole is called by Hegel the "Absolute" and is to be viewed as something spiritual. Hegel then has:
Closely related to Newton's method are Halley's method and Laguerre's method. Both use the polynomial and its two first derivations for an iterative process that has a cubic convergence. Combining two consecutive steps of these methods into a single test, one gets a rate of convergence of 9, at the cost of 6 polynomial evaluations (with Horner rule). On the other hand, combining three steps of Newtons method gives a rate of convergence of 8 at the cost of the same number of polynomial evaluation. This gives a slight advantage to these methods (less clear for Laguerre's method, as a square root has to be computed at each step).
The strategic analysis method is based on the elements or subsystems. This technique is based on prior methods of Frederick Taylor. These subsystems are related to the entire enterprise plan, so if one is changed in modification all the enterprise. This method is divided in four steps. First step is the mission determination in which the managers decide what they want as an enterprise, to be accomplished, what is the main purpose of the company. In this step is also include the principles that will guide the enterprise. The second step is environmental assessment. It is divided in external, determining threats and opportunities, and internal, determining strengths and weaknesses. The third step is objective setting where you create specific goals to the enterprise that can be measurable, achievable, time specific and documented. Finally the fourth step is strategy setting is when the managers create a strategy plan based on the steps before that creates the balance in the company.
Another class of methods is based on converting the problem of finding polynomial roots to the problem of finding eigenvalues of the companion matrix of the polynomial. In principle, one can use any eigenvalue algorithm to find the roots of the polynomial. However, for efficiency reasons one prefers methods that employ the structure of the matrix, that is, can be implemented in matrix-free form. Among these methods are the power method, whose application to the transpose of the companion matrix is the classical Bernoulli's method to find the root of greatest modulus. The inverse power method with shifts, which finds some smallest root first, is what drives the complex ("cpoly") variant of the Jenkins–Traub algorithm and gives it its numerical stability. Additionally, it is insensitive to multiple roots and has fast convergence with order formula_9 (where formula_10 is the golden ratio) even in the presence of clustered roots. This fast convergence comes with a cost of three polynomial evaluations per step, resulting in a residual of , that is a slower convergence than with three steps of Newton's method.
In numerical analysis, the split-step (Fourier) method is a pseudo-spectral numerical method used to solve nonlinear partial differential equations like the nonlinear Schrödinger equation. The name arises for two reasons. First, the method relies on computing the solution in small steps, and treating the linear and the nonlinear steps separately (see below). Second, it is necessary to Fourier transform back and forth because the linear step is made in the frequency domain while the nonlinear step is made in the time domain.
The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. 
The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method.
Dialectic or dialectics (Greek: διαλεκτική, dialektikḗ; related to dialogue), also known as the dialectical method, is at base a discourse between two or more people holding different points of view about a subject but wishing to establish the truth through reasoned arguments. Dialectic resembles debate, but the concept excludes subjective elements such as emotional appeal and the modern pejorative sense of rhetoric.[1][2] Dialectic may be contrasted with the didactic method, wherein one side of the conversation teaches the other. Dialectic is alternatively known as minor logic, as opposed to major logic or critique.
György Lukács, Minister of Culture in the brief Béla Kun government of the Hungarian Soviet Republic (1919), published "History and Class Consciousness" (1923), in which he defined "dialectical materialism" as the knowledge of society as a whole, knowledge which, in itself, was the class consciousness of the proletariat. In the first chapter "What is Orthodox Marxism?", Lukács defined "orthodoxy" as fidelity to the "Marxist method", not fidelity to "dogmas":
Orthodox Marxism, therefore, does not imply the uncritical acceptance of the results of Marx's investigations. It is not the "belief" in this or that thesis, nor the exegesis of a "sacred" book. On the contrary, orthodoxy refers exclusively to method. It is the scientific conviction that dialectical materialism is the road to truth and that its methods can be developed, expanded, and deepened, only along the lines laid down by its founders. (§1)
In his later works and actions, Lukács became a leader of Democratic Marxism. He modified many of his formulations of his 1923 works and went on to develop a Marxist ontology and played an active role in democratic movements in Hungary in 1956 and the 1960s. He and his associates became sharply critical of the formulation of dialectical materialism in the Soviet Union that was exported to those countries under its control. In the 1960s, his associates became known as the Budapest School.