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As Garrett Birkhoff wrote, "John von Neumann's brilliant mind blazed over lattice theory like a meteor". [168] Von Neumann combined traditional projective geometry with modern algebra (linear algebra, ring theory, lattice theory). Many previously geometric results could then be interpreted in the case of general modules over rings. His work ...
John von Neumann (1903–1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath.He had perhaps the widest coverage of any mathematician of his time, integrating pure and applied sciences and making major contributions to many fields, including mathematics, physics, economics, computing, and statistics.
The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable". [ 1 ] : 17 These observables play the role of measurable quantities familiar from classical physics: position, momentum , energy , angular momentum and so on.
Von Neumann's System of Self-Replication Automata with the ability to evolve (Figure adapted from Luis Rocha's Lecture Notes at Binghamton University [6]).i) the self-replicating system is composed of several automata plus a separate description (an encoding formalized as a Turing 'tape') of all the automata: Universal Constructor (A), Universal Copier (B), operating system (C), extra ...
The von Neumann–Wigner interpretation, also described as "consciousness causes collapse", is an interpretation of quantum mechanics in which consciousness is postulated to be necessary for the completion of the process of quantum measurement.
John von Neumann. In set theory, the axiom of limitation of size was proposed by John von Neumann in his 1925 axiom system for sets and classes. [1] It formalizes the limitation of size principle, which avoids the paradoxes encountered in earlier formulations of set theory by recognizing that some classes are too big to be sets.
In von Neumann's cellular automaton, the finite state machines (or cells) are arranged in a two-dimensional Cartesian grid, and interface with the surrounding four cells. As von Neumann's cellular automaton was the first example to use this arrangement, it is known as the von Neumann neighbourhood. The set of FSAs define a cell space of ...
The von Neumann description of quantum measurement of an observable A, when the system is prepared in a pure state ψ is the following (note, however, that von Neumann's description dates back to the 1930s and is based on experiments as performed during that time – more specifically the Compton–Simon experiment; it is not applicable to most ...