International Journal of Theoretical Physics, Apr 1, 1982
Computing processes are ultimately abstractions of physical processes; thus, a comprehensive theo... more Computing processes are ultimately abstractions of physical processes; thus, a comprehensive theory of computation must reflect in a stylized way aspects of the underlying physical world. On the other hand, physics itself may draw fresh insights and productive methodological tools from looking at the world as an ongoing computation. The terminformation mechanics seems appropriate for this unified approach to physics
This chapter contains sections titled: The plane-module, Larger arrays: edge gluing, More states ... more This chapter contains sections titled: The plane-module, Larger arrays: edge gluing, More states per cell: sheet ganging, More dimensions: layer stacking, Display and analysis, Modularity and expandability
this paper, with the same title, was published in the proceedings of the conference ACRI &apo... more this paper, with the same title, was published in the proceedings of the conference ACRI '94: Automi Cellulari per la Ricerca e l'Industria, Rende (CS), Italy, September 29--30, 1994. 9 References
Quantum Communication, Computing, and Measurement 3
The main result of the paper can be summarized as follows. The number of distinguishable quantum ... more The main result of the paper can be summarized as follows. The number of distinguishable quantum states in a 2-dimensional Hilbert space is proportional to the square root of the number of identical copies of each state measured and to the total length of the angle intervals occupied by the state vectors. Surprisingly, it does not depend on the position of the arcs comprising the range on the unit circle. These results can be generalized for the N-dimensional Hilbert space of states of a quantum system.As in the 2-dimensional case, the unit sphere can be reduced to the non-negative orthant of the unit sphere in the real N-dimensional Euclidean space.It turns out [6] that the number of distinguishable states depends only on the area Ω of the domain on the unit sphere from which the states can be chosen, but does not depend on the shape and position of this domain. The optimal distribution is uniform over the domain in angular (polar) coordinates, and the number of distinguishable states is \( W(n,\Omega ) = \Omega (cn)^{\tfrac{{N - 1}} {2}} \) where c is a constant.
Starting from models of particular interest for the physicist, there has evolved in the course of... more Starting from models of particular interest for the physicist, there has evolved in the course of years, with different emphasis and varying degrees of abstraction, a vast literature of mathematical structures known collectively as “general dynamical systems [1].” In this area of investigation, the analysis of particular systems has often led to the study of more general media, i.e., of “host” systems in which a variety of “guest” systems can be embedded. Great conceptual economy and, at the same time, great flexibility, is achieved by considering media that are arbitrarily extended and uniform. For example, while a differential equation of the form x = -f(x) describes a single, isolated oscillator, partial differential equations such as those of the electromagnetic field in a homogeneous medium may be made to describe, with a suitable choice of initial conditions, systems of waves of many kinds, including particle-like “packets” of waves. In the discrete domain, a particular sequential process realized by a specialized piece of hardware, may be reproduced by assigning appropriate initial conditions (stored program) to a more uniformly structured, general-purpose computer.
... Whether my son plays "Pirates" or "Nuns" ... more ... Whether my son plays "Pirates" or "Nuns" is deter-mined not only by his inclinations, but also by what the creators of LEGO saw fit to put in their ... [3] Feynman, Richard, "There is plenty of room at the bottom," reprinted in Microminiaturization (HD Gilbert, ed.), Reinhold (1961). ...
International Journal of Theoretical Physics, Apr 1, 1982
Computing processes are ultimately abstractions of physical processes; thus, a comprehensive theo... more Computing processes are ultimately abstractions of physical processes; thus, a comprehensive theory of computation must reflect in a stylized way aspects of the underlying physical world. On the other hand, physics itself may draw fresh insights and productive methodological tools from looking at the world as an ongoing computation. The terminformation mechanics seems appropriate for this unified approach to physics
This chapter contains sections titled: The plane-module, Larger arrays: edge gluing, More states ... more This chapter contains sections titled: The plane-module, Larger arrays: edge gluing, More states per cell: sheet ganging, More dimensions: layer stacking, Display and analysis, Modularity and expandability
this paper, with the same title, was published in the proceedings of the conference ACRI &apo... more this paper, with the same title, was published in the proceedings of the conference ACRI '94: Automi Cellulari per la Ricerca e l'Industria, Rende (CS), Italy, September 29--30, 1994. 9 References
Quantum Communication, Computing, and Measurement 3
The main result of the paper can be summarized as follows. The number of distinguishable quantum ... more The main result of the paper can be summarized as follows. The number of distinguishable quantum states in a 2-dimensional Hilbert space is proportional to the square root of the number of identical copies of each state measured and to the total length of the angle intervals occupied by the state vectors. Surprisingly, it does not depend on the position of the arcs comprising the range on the unit circle. These results can be generalized for the N-dimensional Hilbert space of states of a quantum system.As in the 2-dimensional case, the unit sphere can be reduced to the non-negative orthant of the unit sphere in the real N-dimensional Euclidean space.It turns out [6] that the number of distinguishable states depends only on the area Ω of the domain on the unit sphere from which the states can be chosen, but does not depend on the shape and position of this domain. The optimal distribution is uniform over the domain in angular (polar) coordinates, and the number of distinguishable states is \( W(n,\Omega ) = \Omega (cn)^{\tfrac{{N - 1}} {2}} \) where c is a constant.
Starting from models of particular interest for the physicist, there has evolved in the course of... more Starting from models of particular interest for the physicist, there has evolved in the course of years, with different emphasis and varying degrees of abstraction, a vast literature of mathematical structures known collectively as “general dynamical systems [1].” In this area of investigation, the analysis of particular systems has often led to the study of more general media, i.e., of “host” systems in which a variety of “guest” systems can be embedded. Great conceptual economy and, at the same time, great flexibility, is achieved by considering media that are arbitrarily extended and uniform. For example, while a differential equation of the form x = -f(x) describes a single, isolated oscillator, partial differential equations such as those of the electromagnetic field in a homogeneous medium may be made to describe, with a suitable choice of initial conditions, systems of waves of many kinds, including particle-like “packets” of waves. In the discrete domain, a particular sequential process realized by a specialized piece of hardware, may be reproduced by assigning appropriate initial conditions (stored program) to a more uniformly structured, general-purpose computer.
... Whether my son plays "Pirates" or "Nuns" ... more ... Whether my son plays "Pirates" or "Nuns" is deter-mined not only by his inclinations, but also by what the creators of LEGO saw fit to put in their ... [3] Feynman, Richard, "There is plenty of room at the bottom," reprinted in Microminiaturization (HD Gilbert, ed.), Reinhold (1961). ...
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