Why not? Exactly because there is nothing tethering our axioms on paper to what is necessarily true. You could formulate something wildly different from ZF±C/Peano/whatever normal axiom system, but we wouldn't call it "math", and what we currently call "math" will work under any conditions

With no mathematical rigor there is no mathematical understanding. You are robbing yourself, as the concepts are meaningless without the context.

Truly appreciate the power of linear approximations by going through algebra, appreciate the tricks of calculus, marvel at the inherent tradeoffs of knowledge with estimator theory, and see the joy of the central limit theorem being true. All of this knowledge is free, and much more interesting than a formal restatement of "it was not supposed to rain, but I see clouds outside, I guess I'll expect light rain instead of a big thunderstorm".

I don't agree at all, vcv rack helped me understand synthesis in a much deeper way than I would have otherwise. What's a retrigger? Oscillator drift? Why do you modulate with a lfo? These are much simpler to understand when you're patching modules by hand in vcv, especially when you start with a blank slate.

On the other hand, before vcv, seeing a vst synth just had me overwhelmed instead.

I'd recommend everyone reading this to get free vcv + the surge vcv library, and just play around with it.

You're in for a nice trip, the concept is called Geometric Algebra:

https://youtu.be/60z_hpEAtD8?si=HHs_9m0IJ43nfI3S (~50m video)

TLDW: Yes, the concept is there, makes much more sense than a cross product (which is just an oriented area) and generalizes really nicely.

Alternatively, read: https://en.m.wikipedia.org/wiki/Bivector

Both can be true.

- Investing provides benefits for society at large - Investors are exploiting the labour of others for their own gain

(but also your examples only work in a very weird worldview where everything is privatised, but I don't want to bother discussing that on this website)