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calculus is irreplaceable for understanding system dynamics. Every meta-stable computer system is an incarnate approximarion of some differential equations rel

calculus is irreplaceable for understanding system dynamics. Every meta-stable computer system is an incarnate approximarion of some differential equations relating the different parts of the system and the way changes propagate from here to there. I don't often use numerical methods, but analysis of stability, classification of fixed point types, topological limits to what small changes to the system can do to the behavior do all come into play. The people enforcing backoff for retries, randomization or careful analysis of fatal vs. temp errors, are using those sorts of insights. while you can take ten years of industry experience to get a feel for these flows, you can also take a good DiffEq/Dynamic systems course and start out understanding the possible shapes at the start.

giantg2 5y ago
I mean, you could call that basic logic and just take a philosophy course. That would provide formal and informal methods of evaluation without the need for actual calculus. This informal understanding and balancing is more closely aligned with philosophy than it is to calculus.
- SamReidHughes 5y ago
  Nope. You could call that basic logic... and you'd be wrong, because it's not basic logic.
  - giantg2 5y ago
    How so? The comment clearly states that they aren't doing any formal calculations, not using numerical methods, and just getting approximate insights. If I'm wrong, show me I'm wrong and post a substantive comment. Snarky comments like that are not inline with HN guidelines.
    - SamReidHughes 5y ago
      It's not a snarky comment, it's literally, not actually basic logic. You had no factual basis for saying it was. Basic logic is here: https://en.wikipedia.org/wiki/Mathematical_logic https://en.wikipedia.org/wiki/Mathematical_logic Dynamical systems has stuff that is not basic logic such as this topological concept which is applicable in understanding how stuff works without doing an actual calculation: https://en.wikipedia.org/wiki/Limit_cycle https://en.wikipedia.org/wiki/Limit_cycle That's calculus. Not logic, not philosophy.
      - giantg2 5y ago
        You misunderstand. This is the basic logic I was talking about. Note my comment mentioned philosophy. Same for limit cycles - they make no mention or this type of calculation. The concept can exist in other domains such as systems thinking. So concepts do exist outside the context of pure math. If you look at everything from a hard math perspective, then that is what you will see. You have to look at the context of the comments to understand. It's not necessarily calculus because the commenter might not be looking at it using those strict theories. There's no support for your assertion that it's not philosophy or not logic. It could coincidentally be similar to a calculus concept, but that doesn't mean that one is using calculus if they are approaching it from a different context that shares a similar concept. https://en.m.wikipedia.org/wiki/Philosophy_of_logic https://en.m.wikipedia.org/wiki/Philosophy_of_logic
        SamReidHughes 5y ago
        Limit cycles are a concrete example of "analysis of stability, classification of fixed point types, topological limits to what small changes to the system can do to the behavior." This is calculus, not logic, not philosophy.
        giantg2 5y ago
        Did they say they're using limit cycles? They could be using less formal methods that are not calculus, like most people do. You have not spoken to the context or approach they are using. Similar concepts can exist in multiple domains with varying levels of formality. Again, any evidence this is not logic or philosophy? Simply saying it isn't, is not a valid argument. Just because you assert a concept exists calculus, does not mean a similar one doesn't exist in another domain/context. Any response to the majority of my comment, especially around context of use? Or are you just trolling by repeating the same line in multiple comments with no substantive support for your claims? Honest question.
    - lanstin 5y ago
      Not doing numerical analysis, but that's not the same as not doing formal analysis. I was thinking of things such as this fascinating paper, particularly the shape of the overall manifold that gives rise to Figure 2: https://sigops.org/s/conferences/hotos/2021/papers/hotos21-s11-bronson.pdf https://sigops.org/s/conferences/hotos/2021/papers/hotos21-s... The insights from these topics: https://en.wikipedia.org/wiki/List_of_dynamical_systems_and_differential_equations_topics https://en.wikipedia.org/wiki/List_of_dynamical_systems_and_...
- rockemsockem 5y ago
  How does logic help you understand what system dynamics will arise from choosing a particular exponential backoff or making a choice about picking some method with a particular known error rate, as the original commenter mentioned?
tonyarkles 5y ago
I realize that I'm in a less common industry, but I often end up using calculus and DiffEqs in my day-to-day work working with drones. To your point on system dynamics, queuing theory pairs really well with calculus on that as well. Being able to somewhat predict how a system is going to behave under load based on measurements and an understanding of how the queues work is super super valuable for decision making.

giantg2 5y ago

I mean, you could call that basic logic and just take a philosophy course. That would provide formal and informal methods of evaluation without the need for actual calculus. This informal understanding and balancing is more closely aligned with philosophy than it is to calculus.

SamReidHughes 5y ago
Nope. You could call that basic logic... and you'd be wrong, because it's not basic logic.
- giantg2 5y ago
  How so? The comment clearly states that they aren't doing any formal calculations, not using numerical methods, and just getting approximate insights. If I'm wrong, show me I'm wrong and post a substantive comment. Snarky comments like that are not inline with HN guidelines.
  - SamReidHughes 5y ago
    It's not a snarky comment, it's literally, not actually basic logic. You had no factual basis for saying it was. Basic logic is here: https://en.wikipedia.org/wiki/Mathematical_logic https://en.wikipedia.org/wiki/Mathematical_logic Dynamical systems has stuff that is not basic logic such as this topological concept which is applicable in understanding how stuff works without doing an actual calculation: https://en.wikipedia.org/wiki/Limit_cycle https://en.wikipedia.org/wiki/Limit_cycle That's calculus. Not logic, not philosophy.
    - giantg2 5y ago
      You misunderstand. This is the basic logic I was talking about. Note my comment mentioned philosophy. Same for limit cycles - they make no mention or this type of calculation. The concept can exist in other domains such as systems thinking. So concepts do exist outside the context of pure math. If you look at everything from a hard math perspective, then that is what you will see. You have to look at the context of the comments to understand. It's not necessarily calculus because the commenter might not be looking at it using those strict theories. There's no support for your assertion that it's not philosophy or not logic. It could coincidentally be similar to a calculus concept, but that doesn't mean that one is using calculus if they are approaching it from a different context that shares a similar concept. https://en.m.wikipedia.org/wiki/Philosophy_of_logic https://en.m.wikipedia.org/wiki/Philosophy_of_logic
      - SamReidHughes 5y ago
        Limit cycles are a concrete example of "analysis of stability, classification of fixed point types, topological limits to what small changes to the system can do to the behavior." This is calculus, not logic, not philosophy.
        giantg2 5y ago
        Did they say they're using limit cycles? They could be using less formal methods that are not calculus, like most people do. You have not spoken to the context or approach they are using. Similar concepts can exist in multiple domains with varying levels of formality. Again, any evidence this is not logic or philosophy? Simply saying it isn't, is not a valid argument. Just because you assert a concept exists calculus, does not mean a similar one doesn't exist in another domain/context. Any response to the majority of my comment, especially around context of use? Or are you just trolling by repeating the same line in multiple comments with no substantive support for your claims? Honest question.
  - lanstin 5y ago
    Not doing numerical analysis, but that's not the same as not doing formal analysis. I was thinking of things such as this fascinating paper, particularly the shape of the overall manifold that gives rise to Figure 2: https://sigops.org/s/conferences/hotos/2021/papers/hotos21-s11-bronson.pdf https://sigops.org/s/conferences/hotos/2021/papers/hotos21-s... The insights from these topics: https://en.wikipedia.org/wiki/List_of_dynamical_systems_and_differential_equations_topics https://en.wikipedia.org/wiki/List_of_dynamical_systems_and_...
rockemsockem 5y ago
How does logic help you understand what system dynamics will arise from choosing a particular exponential backoff or making a choice about picking some method with a particular known error rate, as the original commenter mentioned?

tonyarkles 5y ago

I realize that I'm in a less common industry, but I often end up using calculus and DiffEqs in my day-to-day work working with drones. To your point on system dynamics, queuing theory pairs really well with calculus on that as well. Being able to somewhat predict how a system is going to behave under load based on measurements and an understanding of how the queues work is super super valuable for decision making.