background preloader

Dimension

Dimension
A diagram showing the first four spatial dimensions. 1-D: Two points A and B can be connected to a line, giving a new line segment AB. 2-D: Two parallel line segments AB and CD can be connected to become a square, with the corners marked as ABCD. 3-D: Two parallel squares ABCD and EFGH can be connected to become a cube, with the corners marked as ABCDEFGH. 4-D: Two parallel cubes ABCDEFGH and IJKLMNOP can be connected to become a hypercube, with the corners marked as ABCDEFGHIJKLMNOP. In physical terms, dimension refers to the constituent structure of all space (cf. volume) and its position in time (perceived as a scalar dimension along the t-axis), as well as the spatial constitution of objects within—structures that correlate with both particle and field conceptions, interact according to relative properties of mass—and are fundamentally mathematical in description. The concept of dimension is not restricted to physical objects. A tesseract is an example of a four-dimensional object.

http://en.wikipedia.org/wiki/Dimension_(mathematics_and_physics)

Related:  docs à revoir

Curse of dimensionality The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces (often with hundreds or thousands of dimensions) that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The term curse of dimensionality was coined by Richard E. Bellman when considering problems in dynamic optimization.[1][2] The "curse of dimensionality" depends on the algorithm[edit] The "curse of dimensionality" is not a problem of high-dimensional data, but a joint problem of the data and the algorithm being applied. It arises when the algorithm does not scale well to high-dimensional data, typically due to needing an amount of time or memory that is exponential in the number of dimensions of the data.

Depth = 3rd Dimension Three-dimensional Cartesian coordinate system with the x-axis pointing towards the observer(See diagram description for needed correction.) In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space. My Story: Experimenting With Message Passing Software Modules for Arduino Programming I've been fascinated by the idea of being able to build software applications in a way similar to how electronic circuits are built using ICs. That is, by connecting discrete software components together via clearly defined communication pathways. I've begun to use the Arduino development platform to play around with ideas for implementing this type of component-based system. I'd like to see if it's possible to create useful Arduino-based applications this way.

Duality From Wikipedia, the free encyclopedia Duality may refer to: Mathematics[edit] Manifold The surface of the Earth requires (at least) two charts to include every point. Here the globe is decomposed into charts around the North and South Poles. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be described and understood in terms of the relatively well-understood properties of Euclidean space. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. Length = 2nd Dimension Bi-dimensional Cartesian coordinate system In physics, our bi-dimensional space is viewed as a planar representation of the space in which we move, described as bi-dimensional space or two-dimensional space. History of two-dimensional space[edit]

Playing Book « Tilt In the past, when people spent their spare time reading a book, they read paper books. Nowadays though, people use computers, smart phones, or iPads to read during their spare time. However, electronic books cannot provide the analogue aesthetic which can be felt in a paper book. For example, people cannot feel the texture of the paper, they cannot turn the pages of a book or smell the different scents of paper. Reality Not to be confused with Realty. Philosophers, mathematicians, and other ancient and modern thinkers, such as Aristotle, Plato, Frege, Wittgenstein, and Russell, have made a distinction between thought corresponding to reality, coherent abstractions (thoughts of things that are imaginable but not real), and that which cannot even be rationally thought. By contrast existence is often restricted solely to that which has physical existence or has a direct basis in it in the way that thoughts do in the brain. Reality is often contrasted with what is imaginary, delusional, (only) in the mind, dreams, what is false, what is fictional, or what is abstract.

Vector space Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w. An example of a vector space is that of Euclidean vectors, which may be used to represent physical quantities such as forces: any two forces (of the same type) can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector. In the same vein, but in a more geometric sense, vectors representing displacements in the plane or in three-dimensional space also form vector spaces.

Related: