3 ms·

I dont, no.

wolfram74 7y ago
Numerical methods can be efficient, but nothing beats an analytic method that can be simply evaluated after derived. Often times you can go from an approximate answer with numerous function evaluations to an exact answer in one simpler function evaluation. Pathological cases not withstanding.
- adamnemecek 7y ago
  AD is NOT a numerical method, it's very precise. You can in fact do it on paper as well. https://blog.demofox.org/2014/12/30/dual-numbers-automatic-differentiation/ https://blog.demofox.org/2014/12/30/dual-numbers-automatic-d... Analytical derivatives grow exponentially longer with the length of the expression. AD doesn't have this problem.
  - tntn 7y ago
    Just because automatic differentiation is a different technique than numerical differentiation doesn't mean it isn't a numerical method. (I probably should not say this, but I will anyway: your comments regarding math and science always give me the distinct impression that you know the name of a lot of things without knowing much about the thing. You are frequently breathless about analog quantum computing, Lie algebras, Chu spaces, some universal concept of duality, but then you fail to respond with substantial arguments to people that try to temper the breathlessness. If you want to convince people of things, you should work on this.)
    - adamnemecek 7y ago
      > Just because automatic differentiation is a different technique than numerical differentiation doesn't mean it isn't a numerical method. It does mean that. Pls see the overview paper http://jmlr.org/papers/volume18/17-468/17-468.pdf http://jmlr.org/papers/volume18/17-468/17-468.pdf in particular section "2.1 AD Is Not Numerical Differentiation" > substantial arguments to people that try to temper the breathlessness Which arguments in particular? > our comments regarding math and science always give me the distinct impression that you know the name of a lot of things without knowing much about the thing. Ok be more specific, which ones do you care about? Maybe I don't always have time to answer everyone. > some universal concept of duality It's the concept of adjointness. And yes, it's very universal.
      - tntn 7y ago
        Huh, interesting. First time I read this comment, it said something like "why should I care what you think?" I guess the edit indicates that you do care?
        adamnemecek 7y ago
        No, I edited it because HN has reached out to me many times before that I need to be less of an asshole or I'll get banned. So no, I don't care about what you think, but I don't want to get banned. Anyway, nice that you read the first version but still didn't respond to the other questions.
formalsystem 7y ago
I don't understand why this is being downvoted. It's not like doing division in long form is that meaningful.
- petschge 7y ago
  It is still important to know, even if most division problems you encounter are handed of to a calculator or computer. Why? Because understanding long division is a required background for understanding polynomial division. And understanding that is required to understand how you can get all root of a polynomial using Newtons method. And that is required to figure out how many different plasma modes there are. And THAT is a problem no computer can simply answer for you. Of course only a small number of people care and we don't teach about plasma modes in school, but we teach the basics that you need to start your way towards more complicated things. Long division of polynomials is also used in the construction of CRC sums. So no, understanding long division is not meaningless. It give you a starting point for a lot of other things.

I dont, no.

Numerical methods can be efficient, but nothing beats an analytic method that can be simply evaluated after derived. Often times you can go from an approximate answer with numerous function evaluations to an exact answer in one simpler function evaluation. Pathological cases not withstanding.

adamnemecek 7y ago
AD is NOT a numerical method, it's very precise. You can in fact do it on paper as well. https://blog.demofox.org/2014/12/30/dual-numbers-automatic-differentiation/ https://blog.demofox.org/2014/12/30/dual-numbers-automatic-d... Analytical derivatives grow exponentially longer with the length of the expression. AD doesn't have this problem.
- tntn 7y ago
  Just because automatic differentiation is a different technique than numerical differentiation doesn't mean it isn't a numerical method. (I probably should not say this, but I will anyway: your comments regarding math and science always give me the distinct impression that you know the name of a lot of things without knowing much about the thing. You are frequently breathless about analog quantum computing, Lie algebras, Chu spaces, some universal concept of duality, but then you fail to respond with substantial arguments to people that try to temper the breathlessness. If you want to convince people of things, you should work on this.)
  - adamnemecek 7y ago
    > Just because automatic differentiation is a different technique than numerical differentiation doesn't mean it isn't a numerical method. It does mean that. Pls see the overview paper http://jmlr.org/papers/volume18/17-468/17-468.pdf http://jmlr.org/papers/volume18/17-468/17-468.pdf in particular section "2.1 AD Is Not Numerical Differentiation" > substantial arguments to people that try to temper the breathlessness Which arguments in particular? > our comments regarding math and science always give me the distinct impression that you know the name of a lot of things without knowing much about the thing. Ok be more specific, which ones do you care about? Maybe I don't always have time to answer everyone. > some universal concept of duality It's the concept of adjointness. And yes, it's very universal.
    - tntn 7y ago
      Huh, interesting. First time I read this comment, it said something like "why should I care what you think?" I guess the edit indicates that you do care?
      - adamnemecek 7y ago
        No, I edited it because HN has reached out to me many times before that I need to be less of an asshole or I'll get banned. So no, I don't care about what you think, but I don't want to get banned. Anyway, nice that you read the first version but still didn't respond to the other questions.

formalsystem 7y ago

I don't understand why this is being downvoted. It's not like doing division in long form is that meaningful.

petschge 7y ago
It is still important to know, even if most division problems you encounter are handed of to a calculator or computer. Why? Because understanding long division is a required background for understanding polynomial division. And understanding that is required to understand how you can get all root of a polynomial using Newtons method. And that is required to figure out how many different plasma modes there are. And THAT is a problem no computer can simply answer for you. Of course only a small number of people care and we don't teach about plasma modes in school, but we teach the basics that you need to start your way towards more complicated things. Long division of polynomials is also used in the construction of CRC sums. So no, understanding long division is not meaningless. It give you a starting point for a lot of other things.