3 ms·

I think that was just saying "more space between initial gliders implies a longer time needed to complete construction". There's no Einsteinian relativity to be

by dvgrn 4y ago

I think that was just saying "more space between initial gliders implies a longer time needed to complete construction". There's no Einsteinian relativity to be found here. (A Doppler effect does show up in Conway's Life sometimes, but that's about as far as we get with analogies to the physical universe...!)

westurner 4y ago
How nonlocal are the entanglements in Conway's game of cellular automata, if they're entanglements with symmetry; conservation but emergence? TIL about the effect of two Hadamard gates upon a zero. Quantum discord: https://en.wikipedia.org/wiki/Quantum_discord https://en.wikipedia.org/wiki/Quantum_discord : > In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement. From "Convolution Is Fancy Multiplication" https://news.ycombinator.com/item?id=25194658 https://news.ycombinator.com/item?id=25194658 : > FWIW, (bounded) Conway's Game of Life can be efficiently implemented as a convolution of the board state: https://gist.github.com/mikelane/89c580b7764f04cf73b32bf4e94fd3a3#file-game_of_life-py-L113 https://gist.github.com/mikelane/89c580b7764f04cf73b32bf4e94... Conway's Game is a 2D convolution; without complex phase or constructive superposition. Convolution theorem: https://en.wikipedia.org/wiki/Convolution_theorem https://en.wikipedia.org/wiki/Convolution_theorem : > In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms. From Quantum Fourier transform: https://en.wikipedia.org/wiki/Quantum_Fourier_transform https://en.wikipedia.org/wiki/Quantum_Fourier_transform : > The quantum Fourier transform can be performed efficiently on a quantum computer with a decomposition into the product of simpler unitary matrices. The discrete Fourier transform on 2^{n} amplitudes can be implemented as a quantum circuit consisting of only O(n^2) Hadamard gates and controlled phase shift gates, where n is the number of qubits.[2] This can be compared with the classical discrete Fourier transform, which takes O(n*(2^n)) gates (where n is the number of bits), which is exponentially more than O(n^2).

by dvgrn 4y ago

westurner 4y ago

How nonlocal are the entanglements in Conway's game of cellular automata, if they're entanglements with symmetry; conservation but emergence? TIL about the effect of two Hadamard gates upon a zero. Quantum discord: https://en.wikipedia.org/wiki/Quantum_discord https://en.wikipedia.org/wiki/Quantum_discord : > In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement. From "Convolution Is Fancy Multiplication" https://news.ycombinator.com/item?id=25194658 https://news.ycombinator.com/item?id=25194658 : > FWIW, (bounded) Conway's Game of Life can be efficiently implemented as a convolution of the board state: https://gist.github.com/mikelane/89c580b7764f04cf73b32bf4e94fd3a3#file-game_of_life-py-L113 https://gist.github.com/mikelane/89c580b7764f04cf73b32bf4e94... Conway's Game is a 2D convolution; without complex phase or constructive superposition. Convolution theorem: https://en.wikipedia.org/wiki/Convolution_theorem https://en.wikipedia.org/wiki/Convolution_theorem : > In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms. From Quantum Fourier transform: https://en.wikipedia.org/wiki/Quantum_Fourier_transform https://en.wikipedia.org/wiki/Quantum_Fourier_transform : > The quantum Fourier transform can be performed efficiently on a quantum computer with a decomposition into the product of simpler unitary matrices. The discrete Fourier transform on 2^{n} amplitudes can be implemented as a quantum circuit consisting of only O(n^2) Hadamard gates and controlled phase shift gates, where n is the number of qubits.[2] This can be compared with the classical discrete Fourier transform, which takes O(n*(2^n)) gates (where n is the number of bits), which is exponentially more than O(n^2).