Waypoint 1
Waypoint 1
A genetic algorithm can be used as a search method or modeling evolutionary systems
can build interesting structures, known as individuals
Classicial argument about genetic algorithm performance had three components
independent sampling is provided by large populations that are initialized randomly
high-fitness individuals are preserved through selection, and this biases the sampling process towards regions of high fitness
crossover combines partial solutions, called "building blocks," from different strings onto the same string, thus exploiting the parallelism provided by maintaining a population of candidate solutions.
A partial solution is taken to be a hyperplane in the search space of strings called a schema (This line confuses me, and I'm not sure what the author means by it)
Claim: genetic algorithms are that schemas capture important regularities in many search spaces, and that a form of “implicit parallelism” exists because one fitness evaluation of an individual comprised of l bits implicitly gives information about the 2^l schemas, or hyperplanes
Schema theorem: the genetic algorithm operations guarantee exponentially increasing samples of the observed best schemas in the next time step
The strength of the genetic algorithm lies in its ability to manipulate many parameters simultaneously, used in different applications like aircraft design, tuning parameters for algorithms that detect and track multiple signals in an image, and locating regions of stability in systems of nonlinear difference equation
inappropriate: find the exact global optimum
Genetic algorithm can be used as a search method and computational model, for example, in evolutionary systems. When genetic algorithms evolve, it develops structures also known as individuals to represent solutions to complex problems. The genetic algorithm is based loosely on the idea of population genetics, where the population is randomly selected, and there is variation among the population. However, when selection happens, and a new population is created based on the more successful individual of the previous population, there's a probability of mutation, crossover, or changes to the bit string.
There's a classical argument on the performance of the genetic algorithm: independent sampling, given that there's a randomly large population, high-fitness individuals are selected through selection, and crossover combines partial solutions called "building blocks". Further, the schema theorem says that genetic algorithm operations guarantee exponentially increasing samples of the observed best schemas. Moreover, genetic algorithms can be applied to different practices like aircraft design, tuning parameters for algorithms that detect and track multiple signals in an image, and locating regions of stability in systems of nonlinear difference equations. Yet there are solutions that cannot be answered by a genetic algorithm, like the exact global optimum.
Scorning geographical borders and prejudices, the dice game (Würfelspiel) became the predominant format of ludomusical play across the whole of Europe over the latter half of the eighteenth century
are algorithmic, and thus prescriptive rather than descriptive: rather than merely representing symbolic data, they program procedures.
provide users with instructions on how to tally dice rolls in order to assemble successive measures of simple compositions in popular dance genres
The methods by which Würfelspiele incorporate the operations of chance expose unwritten rules of play in the form of stable harmonic and syntactical features that are designed to accommodate and process the contingency of melodic and rhythmic variation
Caillois claimed, the outcome of play must not be knowable in advance, then a paradoxical question emerges: How can uncertainty be guaranteed? activities that Caillois Lled under the category of alea include coin-tossing, roulette, and lotteries, all of which rely on rigid formal or material constraints that resist manipulation by the player (or anyone else) by denying access to crucial elements of information and control, which are instead distributed across the ludic system.
Do the operations of chance unfold in the name of destiny, exigency, and fate or capricious happenstance What accounts for the blind inconstancy of the world? Might causeless instability itself be responsible for the emergence of (dis)order and (mis)fortune?
Würfelspiele might seem to occupy the opposite end of this spectrum, their epistemological frameworks share the same premises while elucidating the mechanisms by which previously unheard musical material can be spontaneously generated
Würfelspiel illustrated how unpredictable, unrepeatable, and yet commutable events can take place both despite and owing to the principles held to account for them, whether mathematical or divine
Just as Kirnberger’s Der allezeit fertige Polonoisen- und Menuettencomponist produced music for pleasure via mathematical ingenuity and Bach’s Einfall injected an element of levity into the ostensibly serious business of invertible counterpoint, the ambivalent and even ironic tone of pedagogical methods such as Kirnberger’s and Galeazzi’s called into question the time-honored opposition of the entertaining and the didactic, the popular and the esoteric, the trivial and the learned.
The playfulness of Würfelspiele might prompt us to question the opposition of mechanical procedures and improvisatory processes in terms of their systemic properties. In Luhmann’s terms, a game—like a computer—is an operationally closed system in that its high degree of internal order, articulated according to rules and facilitated by conditions that allow for the efficient transmission of information via strictly defined channels for input and output, comes at the expense of openness to its environment.
With regard to improvised conduct, conversely, the opposite is generally assumed to be the case: the openness of a system to external input and contingency reduces its capacity for self-organization and regulation. When ludic and musical players are brought into the equation as interactive agents at the interfaces of such systems, however, these distinctions have to be multiplied and redefined within complex and highly ramified networks.
Tables collect and classify information according to its functions, transforming a one-dimensional stream of data into a two-dimensional mapping of its attributes. In representing a particular class of musical object, a tabular row or column in a Würfelspiel can be read collectively to determine both the constancy and variability of its elements, allowing the analytically-minded observer to distinguish between structural and ornamental components by reconstructing the logic obscured by the juxtaposition of notated fragments on the page.
From my understanding, Würfelspiel is a 18th centruy musical dice game where there are tables of musical fragments inscribed by the dice roll. According to the dice, players would be able to compose a musical piece like minuets and polonaises. However, the takeaway from Würfelspiel is its a algorithmic system and depends on harmonic and syntactical frameworks.
Comparing the work of Kirnberger’s Der allezeit fertige Polonoisen- und Menuettenkomponist and Bach’s Einfall to Würfelspiel, tested the traditional opposition between entertainment and mechanical procedures with improvisatory processes. Moreover, Würfelspiel is just like a game or a computer because it is a closed system. The tables play a significant role in mapping musical fragments from one dimension to two dimensions. This allows people to differentiate the structural and ornamental components through the reconstruction of musical fragments on a page.