Posted: May 26, 2019 7:43 pm
The second sentence does not follow from the first.
The fact that Euclidean geometry contains axioms that aren't necessarily reflective of the real world doesn't stop you landing a shuttle on the moon using it.
A mathematician might say that such and such is the consequence of Euclidean geometry, but not of non-Euclidean geometry (a trivial example being the parallel postulate itself), but this has nothing to do with hiding holes or patching over them. Some groups are abelian and some are non-abelian, both have their own group theory and prove different results. This is a feature, not a bug. In that case real world objects of interest to scientists are successfully modelled by both structures.
Of course from the (purist) mathematician's point of view applicability is neither here nor there.
From your tone I get the feeling you're trying to pick fault with something that you don't understand, rather than trying to understand it. FWIW I'm not sure you'll get terribly far with that approach.
The fact that Euclidean geometry contains axioms that aren't necessarily reflective of the real world doesn't stop you landing a shuttle on the moon using it.
A mathematician might say that such and such is the consequence of Euclidean geometry, but not of non-Euclidean geometry (a trivial example being the parallel postulate itself), but this has nothing to do with hiding holes or patching over them. Some groups are abelian and some are non-abelian, both have their own group theory and prove different results. This is a feature, not a bug. In that case real world objects of interest to scientists are successfully modelled by both structures.
Of course from the (purist) mathematician's point of view applicability is neither here nor there.
From your tone I get the feeling you're trying to pick fault with something that you don't understand, rather than trying to understand it. FWIW I'm not sure you'll get terribly far with that approach.