4 ms·

Interestingly enough, the concept of placing gliders at a distance away seems to touch on the relativity of space and time. Here, with space, we are also encodi

by ivoras 4y ago

Interestingly enough, the concept of placing gliders at a distance away seems to touch on the relativity of space and time. Here, with space, we are also encoding the time at which a certain pattern (a glider) appears where it's needed. In a rigid system like the GoL, we can't trade space with time easily, since everything happens at a constant speed, but it makes one wonder...

bewresu 4y ago
...if there's a GoL version where time varies somehow¹ with something² ¹ directly? ² amount of activity? mass?
- dvgrn 4y ago
  There have been a lot of GoL variants over the years, but I don't remember running into any attempts to vary the speed of evolution in different locations on the same grid. The idea that all neighbors move to the next tick simultaneously is a fundamental assumption in cellular automata in general. If you try changing that, the optimizations that allow us to simulate CAs at any kind of reasonable speed ... all stop working, pretty much. It's kind of painful even to think about. Which means there are probably very interesting rules out there somewhere, where CAs run faster/slower depending on pattern density -- it's just going to be very tricky to explore that particular search space.
  - westurner 4y ago
    The "superstep" that we practically impose upon simulations of entropy and emergence is out of accord with our modern understanding of non-regularly-quantizable spacetime. The debuggable Von Neumann instruction pipeline precludes "in-RAM computing" which conceivably does converge if consensus-level error correction is necessary.
    - OscarCunningham 4y ago
      The term 'superstep' reminds me of the HashLife algorithm https://en.wikipedia.org/wiki/Hashlife https://en.wikipedia.org/wiki/Hashlife for computing the Game of Life. It computes multiple generations at the same time, and runs at different speeds in different parts of the universe, but only with the purpose of computing CGoL faster, not to introduce any relativity.
  - hansworst 4y ago
    Well, there is SmoothLife (e.g. https://www.arxiv-vanity.com/papers/1111.1567/#S4 https://www.arxiv-vanity.com/papers/1111.1567/#S4) where the time step is also made continuous. I suppose you could extend this so that this isn't some uniform value across the entire space, but instead a value that is constantly recomputed based on neighbourhood density.
andrepd 4y ago
How does it "touch on relativity of space and time"?
- 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).
deleted 4y ago
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mannykannot 4y ago
Far from being relativistic, it is a miniature simulated universe with a rigid flat geometry and a universal clock. it is interesting precisely because it is very simple and yet permits remarkably complex events.

by ivoras 4y ago

bewresu 4y ago

...if there's a GoL version where time varies somehow¹ with something² ¹ directly? ² amount of activity? mass?

dvgrn 4y ago
There have been a lot of GoL variants over the years, but I don't remember running into any attempts to vary the speed of evolution in different locations on the same grid. The idea that all neighbors move to the next tick simultaneously is a fundamental assumption in cellular automata in general. If you try changing that, the optimizations that allow us to simulate CAs at any kind of reasonable speed ... all stop working, pretty much. It's kind of painful even to think about. Which means there are probably very interesting rules out there somewhere, where CAs run faster/slower depending on pattern density -- it's just going to be very tricky to explore that particular search space.
- westurner 4y ago
  The "superstep" that we practically impose upon simulations of entropy and emergence is out of accord with our modern understanding of non-regularly-quantizable spacetime. The debuggable Von Neumann instruction pipeline precludes "in-RAM computing" which conceivably does converge if consensus-level error correction is necessary.
  - OscarCunningham 4y ago
    The term 'superstep' reminds me of the HashLife algorithm https://en.wikipedia.org/wiki/Hashlife https://en.wikipedia.org/wiki/Hashlife for computing the Game of Life. It computes multiple generations at the same time, and runs at different speeds in different parts of the universe, but only with the purpose of computing CGoL faster, not to introduce any relativity.
- hansworst 4y ago
  Well, there is SmoothLife (e.g. https://www.arxiv-vanity.com/papers/1111.1567/#S4 https://www.arxiv-vanity.com/papers/1111.1567/#S4) where the time step is also made continuous. I suppose you could extend this so that this isn't some uniform value across the entire space, but instead a value that is constantly recomputed based on neighbourhood density.

andrepd 4y ago

How does it "touch on relativity of space and time"?

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).

deleted 4y ago

[deleted]

mannykannot 4y ago

Far from being relativistic, it is a miniature simulated universe with a rigid flat geometry and a universal clock. it is interesting precisely because it is very simple and yet permits remarkably complex events.