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## Ansatz: … but first of all, let us begin with the inspiration …

2013 June 11

Introduction: The study of physics requires both scientific observation and philosophy. The tenants of science and its axioms of operation are not themselves scientific statements, but philosophical statements. The profound philosophical insight precipitating the birth of physics was that scientific observations and philosophical constructs, such as logic and reasoning, could be married together in a way that allowed one to make predictions of observations (in science) based on theorems and proofs (in philosophy). This natural philosophy requires a philosophical ‘leap’, in which one makes an assumption or guess about what abstract framework applies most correctly. Such a leap, called Ansatz, is usually arrived at through inspiration and an integrated usage of faculties of the mind, rather than a programmatic application of certain axioms. Nevertheless, a programmatic approach allows enumeration of the details of a mathematical system. It seems prudent to apply a programmatic approach to the notion of Ansatz itself and to clarify its process metaphysically, in order to gain a deeper understanding of how it is used in practice in science; but first of all, let us begin with the inspiration.

In physics and mathematics, an ansatz (initial placement of a tool at a work piece) is an educated guess that is verified later by its results.

An ansatz is the establishment of the starting equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution. It can take into consideration boundary conditions. After an ansatz has been established (constituting nothing more than an assumption), the equations are solved for the general function of interest (constituting a confirmation of the assumption).

http://en.wikipedia.org/wiki/Ansatz

Ansatz
An ansatz is an assumed form for a mathematical statement that is not based on any underlying theory or principle.

An example from physics is the Bethe Ansatz (Müller).

http://mathworld.wolfram.com/Ansatz.html