
This is not really (heh) correct. At the least, it’s lazy thinking. But truly, it’s just wrong enough to seem pat and true to Mastodon types but is even more misleading than the supposedly-confusing ideas it’s attempting to illuminate.
The problem is that complex numbers are not secretly just real numbers. Though they are a larger algebraic system that can be faithfully represented using real pairs or special real matrices, the posts above confuse the fact that you can represent complex numbers using real-number machinery with the incorrect idea that complex numbers are truly nothing but ordinary real numbers. A metaphor that perhaps this doof could understand: GPS coordinates are not the city. You can encode every place in a city with two numbers, but the city is not secretly just a system of coordinates. The coordinates are a way of keeping track of something else. And the same is the case here. A real pair or matrix model is a way of (only) encoding complex numbers, not a proof that complex numbers were ordinary reals all along. I mean, duh. If you’re not a dipshit.
So that part of the posts is 100% wrong. A representation is not the same thing as an identification. Encoding complex numbers as pairs or matrices does not somehow convert them back into the real numbers. All it shows is that the complex numbers can be realized as a structured extension built from real components.
And I know this at least partially because standard quantum mechanics requires complex numbers. There are indeed physics-equivalent reformulations using only real quantities, but these work only if you add extra structure that is basically smuggling in complex numbers by the back door (that don’t correspond to the world as it apparently is), so just reals is not enough.
I hate this typical Mastodon intellectual clownishness. So fucking worthless.