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I had heard from Barry Barish that (paraphrased from Lex Fridman podcast): In 1916, Einstein noticed that if he wrote the formulas for general relativity in a particular way, they looked a lot like the formulas for electricity and magnetism. He knew that electricity and magnetism had waves. So he said if the formulas looked similar, then gravity probably has waves too.

The hope is that finding such a dictionary may lead to similar insights about whatever equation / expression of relationships one is starting with.

I want to find a dictionary that lists equations across disciplines that are isomorphic/equivalent to one another. For example:

Physics: $$F=ma$$

Electronics: Ohms law: $$V=iR$$

Physics: Hooke’s law: $$F=-kx$$

And so on (preferably way more disciplines and sub disciplines and math sub disciplines)

Would love any help whatsoever!

Hmm
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    We categorise certain kinds of relationships - for example, if you hold one variable fixed then all of those equations are linear relationships, as opposed to all the many, many different classes of non linear – FShrike Sep 05 '21 at 22:18
  • @FShrike Thank you for that tip! Is there some resource on the taxonomy of relationships I could find? – Hmm Sep 05 '21 at 22:21
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    Personally I don’t know such a thing, but after a quick browse I find that the Wikipedia page on “Relation (mathematics)” is extremely specific and not in general about what you’re looking for. Words like symmetry and duality are perhaps also useful to your search, but again I’m not sure – FShrike Sep 05 '21 at 22:23
  • I don't think that "equivalence-relations" are going to help in your search. – Somos Sep 06 '21 at 01:35
  • @FShrike Thank you! Didn't know about duality. – Hmm Sep 06 '21 at 02:15
  • @Somos Thank you for the suggestion, I will delete it from the tags. What tags would you suggest? – Hmm Sep 06 '21 at 02:15
  • This is not a mathematics question. However Buckingham pi theorem may help you. – Somos Sep 06 '21 at 02:38

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