If that's what passes for aspiration these days then the labour movement truly is dead.

I'm looking for the next thing I want to learn, and have been leaning towards logic programming and theorem provers, so you inadvertently piqued my interest.

I can see another language having a more expressive type system, I've come up against the limitations of Rust's type system more than once, but the tradeoff isn't worth it if I have to go 20 years back in time in terms of tooling.

Yes, the CCP can say jump and expect their corporations to do so, but when everyone in a modern economy jumps at the same time, massive oversupply is the result. More market-based economies are also prone to similar overproduction when everyone gets caught up in the same mania (see AI datacenters), but investors will eventually stop lighting their money on fire when it becomes clear that the returns aren't there. Chinese companies, on the other hand, will just keep jumping until the CCP decides that they are done jumping.

Our feedback loop is geared towards only doing things that provide a return on investment. Their feedback loop has things like social stability and global competitiveness as competing goals to actually doing productive work.

Yes, they are able to accomplish a tremendous amount when they set their minds to it, but doing a tremendous amount more of something than there is actual demand is waste, the opposite of efficiency.

https://www.reuters.com/investigations/china-is-sending-its-...

That might not be the best example to use here because the incentives are entirely backwards. The people claiming to have ESP were doing it for fame and money, whereas the scientists and medical professionals claiming that ivermectin was effective for treating COVID were doing it in spite of the professional stigmatisation that came with it. The unscrupulous would have been shilling for pharma as they always have, that's where the money is, not sticking their necks out for some off-patent drug.

Thank you for this delightful word.

It's not just an area though, it's an area with orientation and magnitude. It's the complex exponential function extended to 3 dimensions.

>By "unpedagogical" I mean: very hard to learn, and even when you learn it, often hard to explain. It's information that doesn't compress well, generalize well, or really convey direct understanding of what's going on. Maybe not the best word for this. Really, I just mean "bad".

I can see where you're coming from on the learning part. There are as many different ways of learning GA as there are teachers, and this does hold it back.

>To me it's incomplete knowledge; it needs to be improved upon so that it makes more sense for people who need to know it. In doing so it will also become easier to learn.

I wish you luck, and I hope that I find it on here someday.

This paper [1] claims to have inverses for general multivectors up to a certain dimension, but I've never needed them and haven't dived into it. I'm curious what the applications would be for general multivectors, I've never come across them in practice.

1 - https://www.sciencedirect.com/science/article/abs/pii/S00963...

Does this word mean "not the way things mathematicians teach things"? My experience has been that mathematicians teach things that are useful to mathematicians to students who are not going to be mathematicians and would be better served learning other things. I wasted countless hours of my life finding analytical solutions to toy calculus problems in a universe that will never yield to those methods.

>My stance on quaternions is that they are an opaque representation of what they are trying to do, which makes them unnecessarily-difficult and annoying. Not to mention hard to learn to visualize.

I've seen some remarkably confusing attempts to understand and visualize these things. This has always baffled me because the equivalent objects in geometric algebra aren't that hard to understand. I really think this is a problem with your pedagogy. You've hidden the geometric meaning of the bivector components in these imaginary components, i,j,k, and you have to take it on faith that i*j=k and instead of it being just the product of two bivector blades.

>The notion of an exponential map and exponentiating generators is, IMO, much more "natural" and intuitively straightforward than the alternatives.

That's because you learned it that way. Exponentiating an oriented area to generate a rotation is perfectly intuitive to me, and I'm not sure how somebody could be confused by the fact that a bivector can be an oriented area or the logarithm of a rotation because it's a simple matter of context.

As to which is more fundamental, I don't think it matters. You could argue that the dot and exterior products are more fundamental because the geometric product is their sum (for vectors). You could also argue that the geometric product is more fundamental because it is simply the Cartesian product of two multivectors, and you derive the dot, exterior and commutator products by filtering that product by grade. Both definitions are true, and "fundamental" is both a matter of perspective and irrelevant to any practical concern.