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My friend claims that it is totally concievably how Kepler guessed this relationship (although he provides no method of how Kepler might have done it), and also that Kepler's observations are "not that hard". As a challenge, I gave my friend a data table with one column labeled $$x$$, the other $$y$$, and 9 coordinates $$(x,y)$$ which fit the relationship $$x^4=y^3$$. I said "please find the relationship between $$x$$ and $$y$$", and as you might expect he failed to do so.