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These are one of those things which seem trivial and useless but indicate important directions to solving these problems - the travelling salesman one is the on

These are one of those things which seem trivial and useless but indicate important directions to solving these problems - the travelling salesman one is the one I find most interesting where the paper is from October 2023! It makes me wonder if you could you could classify General Relativity as a Galactic Algorithm for solving Newtonian Equations i.e. it's technically more accurate but the complexity outweighs the gains so rocket engineers default to newton instead of einstein.

nimish 3y ago
It really isn't, it's basically just laziness and tradition. You can get a significantly better approximation that is coherent and causal by adding a one or two extra linear equations to basic newtonian gravity (not MOND, GEM) and solve them like electromagnetic equations--which every engineer does regularly. Newton isn't causal and this is a root cause of a lot of the issues: it's used for convenience by people who usually don't understand the loss, and now that computers are many orders of magnitude better you lose little. It's the cargo culting and fear of actually deciding what intractable means that's interesting to compare: numerical GR is only galactic for 1920s computers, not 1970s. Fuerer's multiplication algorithm is, in contrast, still crazy to consider and likely will be for decades to centuries, like other truly galactic algorithms
- eternityforest 3y ago
  It's always amazing to see how many people are making use physics and solving equations in the real world. Doing software and basic embedded there are so many tools and techniques we just don't see in a world where the are are three main classes of algorithm, "very simple", "available on PyPi", and "Only one guy here knows how it works".
  - nimish 3y ago
    I mean embedded is very much physics based in contrast to the web stuff that pays the bills. I can only do very basic embedded but it's always fun to see something tactile and tangible. It also needs a kick in the pants with software. Very much behind the curve and tedious.
    - eternityforest 3y ago
      Depends on what level you're working at. At the entry level jobs(As in, helping a company that has never made a PCB get a small run of IoT gadgets made) you might be working with stuff that's close to what hobbyists use. The software and dev tools are amazing and a joy to use(PlatformIO, ESPHome, Arduino, ESP-IDF, Python), and the there's basically no math, just Ohm's law and simple stuff like that, not any algebra or calculus. Unfortunately those jobs are harder to find and the 45k+ a year stuff everyone wants are jam packed with math, and from what I hear obnoxious vendor specific compilers for crappy ARM chips that don't have connectivity, even though it would only cost $2 more and make the product so much better... What's really weird is that open source hardware uses the obscure chips too. Like... your whole selling point is that people can modify it... use something people already know how to use, with enough features that we can actually do something cool with it.
      - nimish 3y ago
        45k sounds low, but I suspect you aren't US based. Id like to move some of my hobby stuff to FTE but it's more favorable to work in software :)
- autonomousErwin 3y ago
  I would love to learn more about, this have you got any examples adding one or two extra linear equations to NG and solving like EM equations in place of GR? What do you mean by the "loss"?
hermitcrab 3y ago
A galactic algorithm and a non-galactic algorithm should give the same answer to a problem. But the time and memory used will differ. General relativity and Newtonian gravity give very similar answers in some cases (e.g. calculating space craft orbits), but different in others (e.g. the orbit of mercury or light passing near a black hole).
- jvanderbot 3y ago
  Actually, no, a galactic algorithm and nongalactic may give different answers. Consider the TSP problem from TFA, in this case two approximation algorithms were presented, one marginally better, meaning the answer would be different. I believe channel capacity encoding was like this as well, but that is not in my wheelhouse.
  - hermitcrab 3y ago
    I was trying to keep things simple, by talking about algorithms that have precise answers (such as multiplying 2 numbers or sorting a list). In that case you would expect the galactic and nongalactic algorithms to give the same answer, but with different time and space characteristics. Perhaps I should have been clearer.
MichaelMoser123 3y ago
> could classify General Relativity as a Galactic Algorithm for solving Newtonian Equations GPS satellites needs to correct their clocks based on General Relativity. It is a very very small correction, but quite important to the accuracy of the navigation system, so you see general relativity quite below galactic scale. https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gps.html https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gp...

nimish 3y ago

It really isn't, it's basically just laziness and tradition. You can get a significantly better approximation that is coherent and causal by adding a one or two extra linear equations to basic newtonian gravity (not MOND, GEM) and solve them like electromagnetic equations--which every engineer does regularly. Newton isn't causal and this is a root cause of a lot of the issues: it's used for convenience by people who usually don't understand the loss, and now that computers are many orders of magnitude better you lose little. It's the cargo culting and fear of actually deciding what intractable means that's interesting to compare: numerical GR is only galactic for 1920s computers, not 1970s. Fuerer's multiplication algorithm is, in contrast, still crazy to consider and likely will be for decades to centuries, like other truly galactic algorithms

eternityforest 3y ago
It's always amazing to see how many people are making use physics and solving equations in the real world. Doing software and basic embedded there are so many tools and techniques we just don't see in a world where the are are three main classes of algorithm, "very simple", "available on PyPi", and "Only one guy here knows how it works".
- nimish 3y ago
  I mean embedded is very much physics based in contrast to the web stuff that pays the bills. I can only do very basic embedded but it's always fun to see something tactile and tangible. It also needs a kick in the pants with software. Very much behind the curve and tedious.
  - eternityforest 3y ago
    Depends on what level you're working at. At the entry level jobs(As in, helping a company that has never made a PCB get a small run of IoT gadgets made) you might be working with stuff that's close to what hobbyists use. The software and dev tools are amazing and a joy to use(PlatformIO, ESPHome, Arduino, ESP-IDF, Python), and the there's basically no math, just Ohm's law and simple stuff like that, not any algebra or calculus. Unfortunately those jobs are harder to find and the 45k+ a year stuff everyone wants are jam packed with math, and from what I hear obnoxious vendor specific compilers for crappy ARM chips that don't have connectivity, even though it would only cost $2 more and make the product so much better... What's really weird is that open source hardware uses the obscure chips too. Like... your whole selling point is that people can modify it... use something people already know how to use, with enough features that we can actually do something cool with it.
    - nimish 3y ago
      45k sounds low, but I suspect you aren't US based. Id like to move some of my hobby stuff to FTE but it's more favorable to work in software :)
autonomousErwin 3y ago
I would love to learn more about, this have you got any examples adding one or two extra linear equations to NG and solving like EM equations in place of GR? What do you mean by the "loss"?

hermitcrab 3y ago

A galactic algorithm and a non-galactic algorithm should give the same answer to a problem. But the time and memory used will differ. General relativity and Newtonian gravity give very similar answers in some cases (e.g. calculating space craft orbits), but different in others (e.g. the orbit of mercury or light passing near a black hole).

jvanderbot 3y ago
Actually, no, a galactic algorithm and nongalactic may give different answers. Consider the TSP problem from TFA, in this case two approximation algorithms were presented, one marginally better, meaning the answer would be different. I believe channel capacity encoding was like this as well, but that is not in my wheelhouse.
- hermitcrab 3y ago
  I was trying to keep things simple, by talking about algorithms that have precise answers (such as multiplying 2 numbers or sorting a list). In that case you would expect the galactic and nongalactic algorithms to give the same answer, but with different time and space characteristics. Perhaps I should have been clearer.

MichaelMoser123 3y ago

> could classify General Relativity as a Galactic Algorithm for solving Newtonian Equations GPS satellites needs to correct their clocks based on General Relativity. It is a very very small correction, but quite important to the accuracy of the navigation system, so you see general relativity quite below galactic scale. https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gps.html https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gp...