Pure Mathematics is More Applicable than Applied Mathematics

Pure mathematics is more properly applicable to the real world than what we currently call applied mathematics.

Applied mathematics is entrenched in narrative regarding physical causality. Models are made by analogy, in the attempt to capture what is happening. Of course this is not what is happening, it is merely a platonic form of reasoning attached to the guts of what we observe.

But this platonic reasoning becomes more than just the lingua franca. It becomes “how” something supposedly occurs. All causal descriptions are expected to be provided using a rigorous-appearing language. This gives the appearance that the uncovering of cause has occurred in a rigorous fashion.

There is no scientifically legitimate justification for assuming mathematics provides a rigorous foundation for cause and mechanism, beyond anything exceedingly trivial.

This is not the fault of mathematics. Mathematics is an internally consistent framework that reflects a symbolized form of human reasoning. Math never asked to be applied to the guts of physical phenomena. This was the inevitable outgrowth of humans wanting to bring precision to satisfy their desire for causal explanations.

It is the chase for internal cause that is in error. There never has been a physical system in nature running under deterministic machinery. The transgressions found in mathematics, from the appalling braindead way it is taught to its use in our current academic paper mills, all stem from the fake way it is attached to internal cause and effect.

But math has both beauty and applicability when it isn’t forced to sing and dance for mere theater. There are natural structures and properties that can be used to describe what we see at the surface, rather than imposed internally.

And it is the surface where mathematics should be applied. This is where structure and property exist, and thus is what actually exists, because this is what has emerged, and *all* of nature is emergent.

The purity of formal systems, logical foundations, internal consistencies and mathematical objects can be used to formalize the structures and properties we observe. We can look upon mathematical form as a simplified description, not of how something happened or where it came from, but merely how a thing can be described, at the surface, here and now.

Groups, Semigroups, Monoids, Loops, Rings, Fields, Algebras, Lie algebras, Hopf algebras, Galois connections, Toposes, Sheaves, Manifolds, etc.

These are all fundamentally disconnected from the notion of internal cause, which is precisely why they are more applicable to nature than the narrative of internal mechanisms and causality. They don’t pretend to be something they are not.

This is how mathematics should be used.