[HN Gopher] Heaviside's Operator Calculus (2007)
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       Heaviside's Operator Calculus (2007)
        
       Author : joebig
       Score  : 48 points
       Date   : 2024-12-01 18:47 UTC (4 hours ago)
        
 (HTM) web link (deadreckonings.com)
 (TXT) w3m dump (deadreckonings.com)
        
       | dang wrote:
       | Related:
       | 
       |  _Heaviside's Operator Calculus_ -
       | https://news.ycombinator.com/item?id=569934 - April 2009 (6
       | comments)
       | 
       | This is also interesting:
       | https://www.johndcook.com/blog/2022/10/12/operational-calcul...
       | (via https://news.ycombinator.com/item?id=33179121, but no
       | comments there)
        
         | joebig wrote:
         | Thanks! It is to the peculiar irrereverance & technical
         | idiosyncrasies of Oliver Heaviside (aka his genius) that we owe
         | the early leaps in the applications of Maxwell's nascent
         | electromagnetic theory.
        
       | mcnamaratw wrote:
       | Great. Possibly missed the opportunity to point out that
       | Heaviside's method is more or less the same as Laplace
       | transforms.
        
         | beautifulfreak wrote:
         | You must have missed this: "In the end Laplace transforms,
         | easier to use with a more rigorous structure and incorporating
         | the powerful tool of convolution, overtook the operational
         | calculus of Heaviside, and his methods largely fell victim to
         | history."
        
           | mcnamaratw wrote:
           | Thanks. Agreed, that could have been a good point to mention
           | that Laplace transforms are more or less the same as
           | Heaviside's method. As I read it, the article leaves the
           | opposite impression instead.
        
       | codr7 wrote:
       | There are several similar variants of different kinds of math
       | that make just as much sense as mainstream methods to me. It all
       | feels very arbitrary.
       | 
       | I think that's what got me into software. If we're just making
       | shit up either way, then useful artifacts is a nice bonus.
        
         | enriquto wrote:
         | But it's the same thing with math. All of science and
         | engineering can be seen as useful artifacts that you obtain as
         | a bonus from math.
        
           | codr7 wrote:
           | Yeah, or air.
           | 
           | Besides, there's plenty more to science and engineering than
           | just math.
        
         | amelius wrote:
         | Maybe start using Roman numerals then?
        
           | codr7 wrote:
           | Roman numerals are obviously inferior, not a fair comparison
           | at all.
        
             | btilly wrote:
             | Roman numerals were designed for a world where calculations
             | were done on an abacus, and numerical systems merely
             | recorded inputs and outputs.
             | 
             | In that world they are better than Arabic numerals, for the
             | simple reason that your brain doesn't have to translate so
             | hard between what you see, and what you record.
        
       | btilly wrote:
       | For a more current example of a mathematical technique that
       | preceded formalization by a considerable amount, consider
       | renormalization. Particularly renormalization over a calculation
       | that takes place over Feynman diagrams.
       | 
       | For decades physicists were happily using this to predict
       | experiment, while mathematicians were tearing their hair out
       | trying to make some formal sense of this, even if only in a
       | limited context. I'd have to do some poking around to find out
       | whether mathematicians are happy about it yet, even though the
       | idea is older than I am.
        
       | 01jonny01 wrote:
       | Gosh this takes me back to my EEE degree. Very difficult to
       | understand at first, way to abstract if you have not seen the
       | electromagnetic phenomena play out in real life and you are not
       | well versed in engineering mathematics.
        
       | selecsosi wrote:
       | I always loved that the derivative of the heavyside operator is
       | equivalent to the dirac delta operator. The idea of impulse and
       | how to apply that to a system is such a unique and useful unlock
       | in E&M and has such a nice analog of connecting the circuit.
       | 
       | One of those things that made it click for me that math truly is
       | defined rules of operations over definitions and could be
       | constructed as to be useful for us, and not just a handed down
       | pure concept. We need to model this very specific thing, here's
       | an operator for it.
        
       | shae wrote:
       | This author published my favorite book on mental math, called
       | Dead Reckoning, you might like it!
        
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