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I have been looking for the answer to that question for a long time, I have spoken with people who according to them "know" about physics, the answers they always give me is "they do it with observations" which seems to me a rather vague answer, I understand perfectly that through observation and experimentation can see certain relationships between magnitudes, but how do they transform that observation into an equation or when they get an idea of ​​how a natural phenomenon can be explained, how do they transform that hypothesis into a coherent and valid equation? , when they say that Newton deduced the equation of the law of universal gravitation as he knew that certain things had to be multiplied, added or raised to a power, etc? I hope someone can give me a satisfactory answer.

JuanJesús
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  • maybe this answer of mine will help https://physics.stackexchange.com/q/262917/ . Euclidiean geometry was the first to tie up specific measurement of the land, with algebraic equations that could make predictions. – anna v Oct 14 '22 at 05:13
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    It's a good question, but I agree with closing it. I don't know how to answer it. You might look at some videos by 3blue1brown. They are about math challenges. But he has some where he explicitly tries to lead you in directions that you could discover the answer yourself. – mmesser314 Oct 14 '22 at 05:57
  • Hi Juan. This sort of question is best discussed in the Physics Stack Exchange chat room. – John Rennie Oct 14 '22 at 06:12
  • See https://en.wikipedia.org/wiki/Dimensional_analysis & https://physics.stackexchange.com/questions/tagged/dimensional-analysis – PM 2Ring Oct 14 '22 at 06:15
  • This is rather like asking how people know any skill : they study for a very long time. Added to that you need a few real geniuses who can think outside the box of their time (but not completely ignoring the box) to make leaps. Lastly the "Good" theories have to pass a very hard exam - repeated testing through careful experiment. We've lots of "bad" theories that, in the absence of experiment, would make very logical and consistent theories that have the "minor" fault that they just don't work. It's all down to many people's hard work and grind often over decades. – StephenG - Help Ukraine Oct 14 '22 at 08:14

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