aap_

9 ms·

61.
by aap_ 2y ago
Probably one of my favorite pieces of software of all times. Learned so much from this!
62.
by aap_ 2y ago
I slightly edited my post while you were writing yours. I'm aware of the article but I still think it could be clearer. I'm a big fan of constructive proofs but that does not seem the case for most mathematicians, so i find a lot
63.
by aap_ 2y ago
Unfortunately there are slightly different but related notions of what spinors are. One key idea is indeed how they transform. A spinor ψ transforms with a transformation S ∈ Spin(n) in a one-sided way: ψ -> Sψ. A vector v in contrast tr
64.
by aap_ 2y ago
What i think is super cool about h3(O) is that you have scalars, a vector and two spinors in one object with the jordan-product giving you all the products between them that have to do with triality. See section 3.4 of John Baez' paper
65.
by aap_ 2y ago
Also not sure I'm understanding you right :) My view is this: the wave function is mere bookkeeping and not anything ontologically fundamental. However the fact that such a seemingly bizarre concept lets you do quantum physics (even if
66.
by aap_ 2y ago
I morally agree, but not quite: think of the wave function as not more than a bookkeeping device. It does get the job done but be careful to ascribe it too high an ontological status! The path integral formulation seems a lot more natural t
67.
by aap_ 2y ago
For a single particle they are easy to confuse. A wave function ψ(t,x) for a single particle gives a probability amplitude to find the particle at coordinate x at time t. In this case one can imagine an amplitude at each point in space and
68.
by aap_ 2y ago
Funny coincidence. I've written a small 3D rendering engine for the ESP32 as well last week. It has standard 3d math, clipping, and rasterization of points, lines and triangles. all in ~1500 lines of code. The repo is not polished yet
69.
by aap_ 2y ago
And 3x3 matrices are 9 dimensional, yet usually you can interpret them perfectly fine with a 3d perspective. The dimension of the algebra is usually not very meaningful if you're trying to gain some intuition about it.
70.
by aap_ 2y ago
I'm curious about your perspective on exterior algebra. So far I've mostly seen it as a special case of GA so my view is probably GA-tinted. I'm just curious how you even do any sort of transformations since the exterior prod
71.
by aap_ 2y ago
No example of such a crackpot is given. The author just claims this without evidence. I've heard this sort of argument before but it's not very clear what it refers to.
72.
by aap_ 2y ago
I think one of the coolest examples is probably classical mechanics. See the SIBGRAPI 2021 videos on https://bivector.net/doc.html
73.
by aap_ 2y ago
The article reads more like a trolling attempt. Geometric/Clifford algebra is incredibly useful and by throwing away its product you lose a lot of the power of the algebra. It's like saying matrix multiplication is not useful and
74.
by aap_ 2y ago
Because quaternions are so cool yet under-appreciated. Unfortunately not many octonion posts.
75.
by aap_ 2y ago
Compulsively checking HN i suppose :D
76.
by aap_ 2y ago
good luck though. my emulator is not particularly user friendly, as in, it has no user interface. i recommend simh (although perhaps not for this thing in particular).
77.
by aap_ 2y ago
XOR is also the basic element-wise multiplication in clifford and cayley-dickson algebras. the way that they differ and which gives them their individual character is all in the sign calculation.
78.
by aap_ 2y ago
I agree. PDP-11 is so much more pleasant, it's not even close. One could make the argument that the addressing modes are conceptually more complicated than what you'd have on a RISC, but the 6502 addressing modes are probably actu
79.
by aap_ 2y ago
Unfortunately i can't. I've been thinking about spinors and related concepts as a hobby for maybe two years now. But i never found an explanation like mine above anywhere. Good geometric intuition about these things does not seem
80.
by aap_ 2y ago
To understand spin it's good to consider a gyroscope. when it has a lot of angular momentum there are two stable states for it in a gravitational field: aligned or anti-aligned with gravitation, up or down. in all other cases the gyros
81.
by aap_ 2y ago
Interestingly showing spherical trig identities was how Hamilton demonstrated his quaternions to the royal irish academy when he found them. See (D) through (K): https://www.maths.tcd.ie/pub/HistMath/People/Ha
82.
by aap_ 2y ago
Wow, pomega is such a terrible name for it!
83.
by aap_ 2y ago
CAR here and CDR just below: https://texdraft.github.io/lisp-1.5/listing.html#line-7626
84.
by aap_ 2y ago
2.11BSD is still a popular choice if you have a PDP-11 (or are emulating one).
85.
by aap_ 2y ago
Why even advertise with "beer" when the link just takes you to a page saying there will be no beer?
86.
by aap_ 2y ago
There are only 7 bits in ASCII. An 8th can be used for parity when transmitting data but a regular program will never see it. Anything above 0x7F is simply not a character.
87.
by aap_ 2y ago
Thanks for "Imaginary Property". I will use this from now on.
88.
by aap_ 2y ago
I think that's a really interesting point. I don't think there are many high level languages where code and data are fundamentally the same kind of thing. I'm aware of only lisp and tcl (funnily there's a thread about tc
89.
by aap_ 2y ago
I would say Ken Thompson and Steve Johnson are the closer.
90.
by aap_ 2y ago
Yeah, no idea how to run the code. There are links to the final demo at the end, but everything else just links to this editor :/

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