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In this lecture by Prof. Frederic Schuller @ 17:49 , it is said that Laplace asked a question if force could be seen equally as curvature of the underlying space which the particle moves in. However, I can't find any reference where I can't seem to find any document stating that Laplace actually stated this. Could I get help finding a reference? Thanks.

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    $\begingroup$ It's at 10:17-12:18, 1749 is the year of Laplace's birth. And you cannot find a reference because it does not exist, Laplace never asked that. Gauss only defined curvature in 1827, the year of Laplace's death, and even that only for surfaces. The "curvature of the underlying space" only made sense after Riemann 30 years later, and even he did not ask that. Maybe Schuller is confusing Laplace with Clifford, who was first. $\endgroup$
    – Conifold
    Commented Jul 6, 2022 at 6:22
  • $\begingroup$ Sounds like another case of Frederick Schuller not knowing the subject he is talking about. $\endgroup$ Commented Jul 6, 2022 at 23:28
  • $\begingroup$ At 25:35 he says that "Laplace found this [i.e. that we can redefine notion of straight line to absorb gravitational force] not using autoparallel equation, because he did not have it". I guess, Schuller meant that Laplace asked a question that in our terminology can be reformulated as a question about curvative space, but he used other terminology. $\endgroup$ Commented Jul 6, 2022 at 23:45
  • $\begingroup$ Laplace was one of the first to propose that gravity had a finite speed: en.wikipedia.org/wiki/Speed_of_gravity#Laplace This also lead him to suggest the idea of a black hole en.wikipedia.org//wiki/Pierre-Simon_Laplace#Black_holes . More details on Laplace's thoughts can be found at mathpages.com/home/kmath690/kmath690.htm. But there is nothing that seems to support Schullers claim. $\endgroup$
    – asmaier
    Commented Feb 23, 2023 at 22:28
  • $\begingroup$ I heard the same said by prof Sean Carroll in this link (min 7:15), youtube.com/…. I think this refers to the fact that the force is the gradient of the potential. $\endgroup$
    – Riad
    Commented May 25 at 23:05

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