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One example that I recently learned of is the use of ordinary differential equations (ODEs) vs. delay equations in mathematical modeling. ODEs are apparently "memoryless" - like how Markov chains are in probability theory - though my classmates and I (not surprisingly) have never considered such a question before, concerning ODEs. However, ODEs are apparently still heavily used because they are so much simpler to deal with.

In general, does this sort of thing happen pretty often in academic research? Do a lot of researchers choose to use inferior tools that are significantly easier to handle? This sort of seems to go against the idea of using cutting-edge tools in academia...

closed as unclear what you're asking by David Ketcheson, Bob Brown, scaaahu, user3209815, Wrzlprmft Feb 10 '17 at 8:26

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    Yes - though I'd argue that being easy to handle renders a tool more valuable than a technically superior but difficult to use tool or method. In bioinformatics, for example, BLAST is one of the most frequently used and cited tools, in part due to its ease of use. – Harry Feb 10 '17 at 0:25
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    The position of a falling object is governed by an ODE, not a DDE. You want to use the appropriate tool, not necessarily the most "powerful" (aka complex) tool. Simpler models are better, provided they capture the phenomena you are interested in. – David Ketcheson Feb 10 '17 at 0:33
  • @DavidKetcheson Good point - fewer parameters generalise better. – Captain Emacs Feb 10 '17 at 0:35
  • In addition to what @DavidKetcheson said: The point of mathematical modelling and dynamical-systems research is most often to understand why and how certain phenomena occur, not to provide an exact model of reality (which is impossible anyway and would require PSDDEs or similar). If an ODE allows us to model a phenomenon sufficiently accurately to understand what is going, that’s better, because we have indeed a better theoretical understanding of ODEs. And from the theoretical point of view, you do of course begin with understanding ODEs before moving to the more complex DDEs. But I digress … – Wrzlprmft Feb 10 '17 at 8:35
  • @user68375: based on your logic, delay equations shouldn't even have to be invented and put into use in current research – How does this follow from my logic? Of course, DDEs are important and necessary to model some systems (at least if you want gain any useful insights), but that does not mean that you should use DDEs for everything. And that’s not even taking into account that there is a huge class of systems where there is no relevant delay or memory whatsoever. – Wrzlprmft Feb 10 '17 at 19:53
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Newton gravitation theory is inferior to Einstein's theory of gravitation, but incredibly more useful for planetary motion, space travel, and most related things unless you go for high precision (GPS), or cosmology etc. Yes, inferior tools are often the right ones to use if they cover many important cases.

Usefulness and simplicity also permit robust use not too dependent on the user's expertise and thus are also often superior from the perspective of error mitigation.

Sometimes even outright wrong theories can be useful, such as Sommerfeld's theory of spectral lines (before it was superseded by Quantum Mechanics, but of course, here the better theory was really preferred). Of course, for atomic physics, as long as no extraordinary accuracy is required, you probably still wouldn't use the full QED.

  • This doesn't answer the question; it debunks the premise of the question. I think the question should be closed as "based on a false premise." – David Ketcheson Feb 10 '17 at 0:36
  • @DavidKetcheson I am not sure I understand. Could you explain in more detail? – Captain Emacs Feb 10 '17 at 10:19

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