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@lirelum.bsky.social
(I am large, I contain multitudes.)
Intellectual property is such a funny concept
Even given the copyright etc. laws we have, physical property is just not an appropriate analogy for how it works
The concepts that fall under it aren’t even particularly similar
Trademarks, patents, and copyright are fundamentally different
Intellectual property is such a funny concept
Even given the copyright etc. laws we have, physical property is just not an appropriate analogy for how it works
The concepts that fall under it aren’t even particularly similar
Trademarks, patents, and copyright are fundamentally different
This is also why we can’t define an angular momentum four vector by the way
Or one way of looking at the reason anyways
Angular momentum is deeply connected with 3d rotations and there’s simply no way to make that fit nicely into 4d space isomorphically
Anyways, I hope that makes it clear why cross products turn up so much relating to rotation
SO(3) is the space of 3d rotations after all
We can actually characterize the dual operation (in three dimensions) by the requirement that a x b = a* • b
You do need to use a metric to actually establish this dual as an isomorphism into ∧^2 R^3, which makes sense because the definition of the dual uses the metric
There exists an isomorphism between vectors and antisymmetric matrices given by the hodge dual, *
We find that a x b = *(*a • *b - *b • *a) = *[*a,*b]
* is a Lie algebra isomorphism
so(3) is the tangent space of the Lie group SO(3) at the identity
It turns out that this tangent space is precisely the space of anti symmetric 3x3 matrices, with the lie product given by commutation of matrices
in fact, (so(3),[*,*]) -> (R^3, *x*) is a lie algebra homomorphism (isomorphism in fact)
in fact, (so(3),[*,*]) -> (R^3, *x*) is a lie algebra homomorphism (isomorphism in fact)
again and again, its the lie algebra for SO(3) hiding in plain sight
always having to do with cross products in some ways (these are the commutation operators for the angular momentum operator components)
how did scientists figure out what dinosaurs were called anyways? it seems very difficult to figure out a name from some bones
i wonder if future archaeologists will be able to look at my bones and figure out that i was called [*************]
some time soon im gonna have to go back and actually learn quantum mechanics instead of just skating by with the born rule and {A,B} -> iħ [A,B] but its honestly working really good so far
i guess thats just a physics thing? i mean i guess it makes sense to be able to write an integral like an operator while still keeping the variable of integration clear
this QFT book im reading puts the dx at the beginning of the integral and it annoys me deeply...
mostly because im not used to it i guess, ill probably be fine with it eventually
the idea of making a boring platformer solely to practice at gamemaking so i can make this thing in my brain that i dont even think id care about selling sort of makes me want to die
i do have an idea for a game ive had rattling around in my brain for a while, but unfortunately, its one of those genres they say you shouldnt attempt as a first and i have no simpler ideas
The phrase “linear time” annoys me because it only ever seems to get used for really weird insults?
i like to think that instead of being a bad person im just an idiot for everything that isnt math but im not super stoked to go find out for sure
every once in a while im confronted with an idea like "x is obvious and everyone who doesnt see that is evil" and then i actually just dont understand it and i resolve to just never speak of that topic ever again in my life
It’s been a while since I had a major depressive episode I think
Raw fish is much better in flavor and Texture than cooked fish
my least favorite part about reading about math on wikipedia is that it will have a near useless "Introduction" section that leaves out all mathematica detail, then immediately jump into "the space of spinors is the fundamental representation of the clifford algebra" with absolutely no connection
Like no shade to philosophy but you have no business talking about quantum mechanics if you can’t explain what a lagrangian is
I “love” it when philosophers who don’t understand how physics works talk about theories in physics
it isnt the same thing as the simulation hypothesis! it doesnt mean the universe is fake!
stupid name confusing everyone...
i hate how people talk about the holographic principle
I have to go in to work very soon, and it is raining quite hard, and all the close parking spots were taken…
in a physical sense
shoes that look good are especially terrible
this post brought to you by working for 7 hours on concrete tiles wearing converse with flat feet
i mean it can probably still work fine, my gut tells me a lorentz transformation is still a canonical transformation because the lagrangian is invariant, but its still less nice
it annoys me deeply that the hamiltonian isnt lorentz invariant, because the hamiltonian formulation is so much nicer and more geometrical than the lagrangian formulation
If ur a beginner to Linux I recommend Qubes os very easy to use and requires little troubleshooting totally promise 100% no lie here
Statistically, it’s difficult to find friends who are like me (doesn’t really care about social interaction, doesn’t have many friends, weirdo)
That’s because people like me don’t have many friends
It turns out you can prove that the linear part of its increment must be zero at an extremum, and hey, the linear part is precisely the first order expansion, and the rest goes to zero as the varying function h goes to zero
Oh my god I finally actually understand how the Euler Lagrange equation is derived
I mean, I knew the derivation obviously, but “we can just ignore all the orders 2 and up in the Taylor expansion because infinitesimals” was… unsatisfying
its annoying to read about calculus of variations
the notation is very sloppy and read literally the stuff people read is halfway nonsense
suggestive at best
i guess thats what physicists get up to
which is fine and all but i need to know the math before i can feel comfortable with that!
you know, my main thought during the middle section of portal 2 was "if only you didnt want to kill me glados, i would happily stay and do tests forever"
That’s true! I don’t manage that every day. Gotta look at the silver lining
I’m kinda bad at feeding myself
So far today I’ve eaten one entire pizza and that’s it
Gaming on Linux is currently very easy for most games, and pretty easy for everything else
It’s been years since something has just not worked
Then again, I am not a big gamer
There might be big blind spots I have. The most demanding game I’ve played is halo.