IIRC there's a fairly natural positive definite quadratic form on GA (used as the canonical norm) that takes the scalar part of the geometric product of a multi-vector and its reverse.
On the other hand, there's the k-th exterior power of the metric where one asks that wedge/interior products be adjoint in order to extend the metric to higher-degree forms.
I was under the impression that these metrics are the same, but maybe I'm completely wrong? Assuming I'm not, then the GA approach seems more natural to me.
> pull out Hodge Duals every time you want to do something that involves the metric, but I'm also unconvinced that geometric algebra is the answer here.
I don't know, I recently tried to work out how the metric on vectors/1-forms induces a metric on higher-degree forms, and if the geometric product magically gives this for free I'd say it's a win (same for the Hodge star).
If you ever wondered how to write a programming language, this is probably the best resource to get started (and then of course Crafting Interpreters).
> In BoC, the equivalent of a message is received by multiple actors and operates with exclusive access to the message and all of the receivers.
(emphasis mine)
IIUC with actors, messages are processed by exactly one actor so it can be difficult to express transactions (e.g. transferring funds from A to B cannot be done atomically). Erlang somewhat fixes this with "selective receive" which re-introduces the possibility of deadlocks. BoC fixes both issues.
Apart from installation problems/crash issues, do you have some feedback about type checking with ty vs. pyrefly? Which is stricter, soundness issues, etc?
Both are rust/open-source/new/fast so it's difficult to understand why I should choose one over the other.
Nice! It would be interesting to visualize the total momentum vector, IIRC Verlet being symplectic should be good at preserving symmetries, whereas RK4 is good at conserving energy.
I've been programming in c++ for 25 years (15 professionally) and I really don't see any reason to keep using it apart from dealing with legacy codebases.
Most arguments in the article boil down to "c++ has the reputation of X, which is partly true, but you can avoid problems with discipline". Amusingly, this also applies to assembly. This is _exactly_ why I don't want to code in c++ anymore: I don't want the constant cognitive load to remember not to shoot myself in the foot, and I don't want to spend time debugging silly issues when I screw up. I don't want the outdated tooling, compilation model and such.
Incidentally, I've also been coding in Rust for 5 years or so, and I'm always amazed that code that compiles actually works as intended and I can spend time on things that matter.
Going back to c++ makes me feel like a caveman coder, every single time.
Yes, but from the canonical form of rotation matrices [1] I would expect such matrices to be represented as a sum of bi-vectors/rotors, which should take the same amount of data?
Geometric Algebra supporters keep advertising that rotors are great since they work in any dimension, which makes me wonder: would an arbitrary n-dimensional SVD-like decomposition benefit from using rotors instead of rotation matrices, and if so how? And if not, why?
> and also faster than it takes me to verify the answer given by the machine.
I always thought there was a kind of NP-flavor to the problems for which LLMs-like AI are helpful in practice, in the sense that solving the problem may be hard but checking the solution must be fast.
Unless the domain can accomodate errors/hallucination, checking the solution (by a human) should be exponentially faster than finding it (by some AI) otherwise there's little practical gain.
On the other hand, there's the k-th exterior power of the metric where one asks that wedge/interior products be adjoint in order to extend the metric to higher-degree forms.
I was under the impression that these metrics are the same, but maybe I'm completely wrong? Assuming I'm not, then the GA approach seems more natural to me.