I just watched George Hart's video https://simonsfoundation.org/multimedia/attesting-to-atoms/ and was left with a vexing disquiet about the fact that the macroscopic structure of crystals seems to imply the existence of atoms and yet gives us no information about how big atoms are. ... I'm not saying it's a believable physical theory, but it seems like it would give an example of a universe with crystals but without atoms. Or is this idea incoherent in some way? Jim Propp --I think Propp is correct. Make a 3x3-symmetric-matrix- valued field throughout your material. Assume there is an energy function which is some integral of some function of the spatial derivatives of the field. Assume matter tries to minimize the energy. Some math of that ilk actually happens in elasticity theory (which theory was devised without assuming or knowing about atoms) so it is physically plausible. The orthonormal eigenvectors of the matrix then serve to transmit information about orientation around from here to there. We can also make a "surface energy" which depends on orientation of surface with respect to these eigenvalues (arises naturally via matrix-vector multiply). Then you'll get crystals which like to have the correct angles, but no atoms needed. So no -- I do not think crystal existence per se proves atoms exist, and indeed in the year 1890 or so, everybody already knew about crystals, plus there was other evidence accumulating like stoichiometry, but atoms still were regarded as in doubt by the Great Minds of the day. However, it seems fairly unnatural to believe in all that compared to (which seems simpler) just buying into atoms, and indeed already the ancient Greeks had invented the atomic concept. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)