I'd define it as the nonphysical controlling the physical. Math is one obvious example of such magic.
Hence why Bacon, who originated modern science by rejecting teleology and promoting math, was an occultist.
Hence why Bacon, who originated modern science by rejecting teleology and promoting math, was an occultist.
By contrast, science is bottom-up--a continuing process of experimentation and analysis. Although scientists have varying beliefs, scientific literature normally makes starting assumptions only insofar as they are helpful to the process--like the (unproven but very helpful) assumption that physical processes obey consistent physical laws that don't change between experiments, or mathematical axioms and their resulting knowledge/methods. But all knowledge obtained scientifically should be held lightly and remain subject to falsification by further experimentation.
There's nothing wrong with top-down knowledge structures built on a set of starting assumptions, as long as we don't "catch" worldviews like the cold without subjecting them to truth tests like correspondence to reality and internal consistency.
In math, a wrong answer isn't so much "wrong" as it is inconsistent with established mathematical properties/rules.
The fact that it often corresponds to our experience of reality is a consequence of thousands of years of refinement with the goal of making it describe reality as closely as possible while remaining internally consistent.
But that doesn't make it any less invented... just a very helpful tool for modeling reality.
I think we can both agree that reality (the physical universe) is well-ordered, self-consistent, and eminently logical in its operation. (Side note: my own belief is that it exhibits these qualities because it reflects the character of its Creator.)
And yes, it obeys certain concepts with absolute constancy - which we have worked to discover and which our mathematical language describes.
But I still maintain that the math and physics knowledge we have is at best limited and at worst an incomplete set of poor approximations. Because they cannot (and I maintain they won’t ever) account for everything we observe, or answer every question we have about the universe, and because its axioms have led to all sorts of abstract structures that have no relation at all to anything ever observed, I still think it’s fair to call math “invented”.
That being said, the real concepts we attempt to grasp in what we observe of the universe are clearly vastly superior to our comparatively small efforts to understand and model them.
Things are true in math if we can follow the rules to derive the truth from axioms. That knowledge may then describe or predict something which should hold true in reality, which is tested via experiments.
The key difference between hydrogen and helium, for instance, seems to be a matter of number.
But wouldn't you say that arithmetic, geometry and harmonics are intrinsic properties of every universe?
The discovery of these properties seems to produce almost magical effects in our world. As it would for every intelligent society discovering these properties.