Yes but also no. One of the most fascinating applications I've seen is here: http://versor.mat.ucsb.edu (and in subsequent work).
There's already a decent tl;dr of the approach on that page, but the tl;dr of that tl;dr is that conformal geometric algebra seems to provide not only a rich language of geometric operations but--importantly!--these operations seem to compose intuitively and interpolate well ("well" in the same way interpolation between quaternions afford the most-natural interpolation between 3D transforms).
The work there uses it to develop tools for parametric design...I'd be very curious to see it extended (e.g. to include time dimensions).
What is notable though is that whereas a lot of the "hype" around geometric algebra revolves around the ostensible intuitiveness--"look, we only need Maxwell's equation, singular, in GA"--actually using it effectively seems to require acquisition of a lot of vocabulary and concepts (e.g. to make use of versor you need to know about blades, rotors, etc.)...the learning curve to use the material is actually steep. That wouldn't prevent it being used as the backend of some tool, but the idea that GA is intuitive and "easier" than alternatives doesn't seem to hold up in practice (IMHO)...at least for uses like these.
Then there's the efficiency issues in that, in general, each term in a k-dimensional geometric algebra will have 2^k coefficients (and thus adding two terms is ~ 2^k operations and multiplying is ~ 2^(k+1))...a good implementation will have a lot of difficult tradeoffs to consider.
It is intuitive and easier in the sense that when you don’t have that vocabulary and bag of concepts – trying to work in some other formalism – all of your arguments end up being much more complicated and cluttered.
As for the number of scalar parameters involved: if anyone wanted to put significant time and money in, as has been done with matrix computation libraries, most of the 0×0 multiplications can be skipped, and the rest can be efficiently SIMDized, etc.
If the concern is bandwidth over the wire, there are often ways to compress things. E.g. we can take the stereographic projection of a rotor and then reduce the precision to save a lot of I/O without losing accuracy.
Thanks for posting this. It's unlikely to get much discussion due to the lack of detail and the poor English (and it is hard to know the context here)...but it's interesting to see this nonetheless.
It's a wonderful luxury to craft such a sufficiently vast work of nonsense that no one possessed of sufficient reason to craft an informed critique will ever feel it worthwhile to invest the time to do so...one can putter away indefinitely in such a self-crafted safe space
Must all creation be judged? Subject to code review? Criticized and torn apart? Next, let us ban the child's doodle, for it is a self-crafted safe space, free of criticism and the harshness of reality.
Yes. Yes. Yes. And Exalted, Loved, and Adored. Critique is not the same as banning. The Child's doodle is always critiqued, which is why we say "Good Job!" to the child who shows us the doodle. The doodle is not created in a self-crafted safe space by any measure.
Creative works are not delicate embers that need to be protected from the elements. They are divine sparks, each one illuminating the darkness. That light is meaningless without eyes to see it.
The child's doodle is something one ca see and understand. You can even try to psychoanalize it or whatever.
What I'm afraid is that there are some really powerful and valuable ideas in Urbit but they will evaporate away from humanity's gasp because there's no way to practically connect them to anything.
Also a child's doodle is something you can ignore or throw away and nothing will be lost... while this has some value in it...
(Edited because I saw they actually have an understandable mathematical formalism for all of it. Sorry for guessing otherwise.)
The creator of this project published a website, took on volunteers to help build it, and held meet-ups to discuss it. In other words, they went well out of their way to publicise it. So yeah, at that point anyone has the right to say anything they like about it. If the author didn't want that to happen, they could have just kept it a private project, never to see the light of day.
Very late to see this but am curious how these approaches handle words with numerous meanings (like run, which arguably has dozens if not hundreds of idiomatic meanings in English).
Distinct vectors for each meaning? One vector and the metric still works better than you'd think? It's not clear from the paper at a skim.
I will set my face against the soul that hath eaten blood, and will cut him off from among his people; for the soul of the flesh is in the blood; and I have given it to you upon the altar to make atonement for your souls, for it is the blood that maketh atonement for the soul. Therefore have I said unto the children of Israel, No soul of you shall eat blood, neither shall the stranger who sojourneth among you eat blood. [Leviticus 17:10-12]
Thank you for being one of the few commentators to not get distracted by the sci-fi!
Nah, Trump and his crew are useful idiots when it comes to Russia; they think they are #1 teaming up with #3 to keep China stuck at #2, when the reality is they are getting tricked by the old "let's you and him fight, partner" gambit.
So, useful idiots, some bought off for stunningly cheap and others true believers or just outright incompetent.
Far likelier than a non-imperialist defense policy will be Flynn finally trying to launch that pre-emptive Christian jihad he's been salivating for, in partnership with Russia.
It would be nicer to see what you see, of course, but I can't what with having familiarity with the people involved.
> Nah, Trump and his crew are useful idiots when it comes to Russia;
Since Eisenhower, which presidents have not been 'useful idiots'? I'd nominate Kennedy and Carter. Someone I respect said that Nixon hated the globalists, but he escalated the war in Vietnam (only ending it after his re-election), and I wasn't alive then so I don't know.
In recent history, Clinton continued G.H.W. Bush's free trade agenda. GW Bush couldn't even read a teleprompter. Obama was good at reading the teleprompter, but didn't have a good understanding of any of the problems he was supposedly addressing.
I think the real useful idiots are those employed by the traditional news media: CNN, NBC, ABC, CBS, etc. They lived in a little bubble, thinking that people really wanted four more years of the Reagan-Bush-Clinton-Bush-Obama status quo.
You have "interesting" and, to be polite, "idiosyncratic" ideas and framing to the point that the expected cost/benefit (for me) of having a real discussion doesn't seem favorable.
Instead, I would offer you some friendly advice: since you have such strong views, I encourage you to write down your political predictions (what you think the new admin will do; what you think will happen as a result; how you think other parties will react, and how those reactions will play out...whatever you think is valuable).
File these predictions away and revisit them at some future date. Keep score!
What did you get right? What did you get wrong? When you get things right, were you right for the reasons you expected to be right, or did you get lucky?
When you get things wrong, was it because you had bad information? Faulty reasoning? Unexpected left-field development not reasonably foreseeable?
Doing this exercise will only serve to sharpen your mind and your understanding!
If you really felt like the possibility of a 'real' discussion was nil, just don't post. taxicabjesus made valid points, and you just condescendingly insult him. For what purpose?
Seconding the question because I want to see the encodings.
Intuitively this makes sense: in the GA formalism a "single" term requires 2^n fields (where n is the spatial dimension), and "simple" operations like addition and multiplication thus require 2^n (or more) operations to evaluate.
If you could instead somehow do those operations in O(1) time you would clearly pick up a rather nice speedup, but again I'm curious what the problems and encodings (as GA) actually look like.
There's already a decent tl;dr of the approach on that page, but the tl;dr of that tl;dr is that conformal geometric algebra seems to provide not only a rich language of geometric operations but--importantly!--these operations seem to compose intuitively and interpolate well ("well" in the same way interpolation between quaternions afford the most-natural interpolation between 3D transforms).
The work there uses it to develop tools for parametric design...I'd be very curious to see it extended (e.g. to include time dimensions).
What is notable though is that whereas a lot of the "hype" around geometric algebra revolves around the ostensible intuitiveness--"look, we only need Maxwell's equation, singular, in GA"--actually using it effectively seems to require acquisition of a lot of vocabulary and concepts (e.g. to make use of versor you need to know about blades, rotors, etc.)...the learning curve to use the material is actually steep. That wouldn't prevent it being used as the backend of some tool, but the idea that GA is intuitive and "easier" than alternatives doesn't seem to hold up in practice (IMHO)...at least for uses like these.
Then there's the efficiency issues in that, in general, each term in a k-dimensional geometric algebra will have 2^k coefficients (and thus adding two terms is ~ 2^k operations and multiplying is ~ 2^(k+1))...a good implementation will have a lot of difficult tradeoffs to consider.