wa wa wa

  • 2 Posts
  • 86 Comments
Joined 1 year ago
cake
Cake day: July 12th, 2023

help-circle


  • Gnome Kat@lemmy.blahaj.zonetoMemes@lemmy.mlsmoking
    link
    fedilink
    English
    arrow-up
    1
    arrow-down
    2
    ·
    edit-2
    26 days ago

    You are the one who presumed to know what I do or don’t actually want. Thank you for your attempt at kindness but it really didn’t come off like that to me. I think its best to end this interaction here as its not going to be productive for either of us. Sorry.

    Edit: oh i thought you were the person who I was responding too but you are not… in that case please leave me alone, thankyou…



  • Gnome Kat@lemmy.blahaj.zonetoMemes@lemmy.mlsmoking
    link
    fedilink
    English
    arrow-up
    7
    arrow-down
    4
    ·
    edit-2
    26 days ago

    im trying very hard to quit smoking weed… i know it’s not the same as nicotine addiction but it’s still a struggle. I smoked weed almost every day for like 6 years or something.

    its annoying cus like i will be reminded of it constantly, weed culture is everywhere, memes and shows and movies and books. I get reminded and i want it, I get the urge and its hard not to smoke a little. i will go days or weeks without any but then I will fuck up and smoke again and suddenly i will be smoking every day again for a few weeks.

    edit: i wasn’t asking for advice, i have a therapist I am working with please stop trying to give me advice its not what I want or need and I don’t like it, it makes me super incredibly uncomfortable. Its not helping. Thank you








  • Gnome Kat@lemmy.blahaj.zonetoScience Memes@mander.xyzteachings
    link
    fedilink
    English
    arrow-up
    2
    ·
    edit-2
    2 months ago

    Oh no, you were right on the money. In G2 you have two basis vectors e1 and e2. The geometric product of vectors specifically is equivalent to uv = u dot v + u wedge v… the dot returns a scalar, the wedge returns a bivector. When you have two vectors be orthonormal like the basis vectors, the dot goes to 0 and you are just left with u wedge v. So e1e2 returns a bivector with norm 1, its the only basis bivector for G2.

    e1e2^2 = (e1e2)*(e1e2) = e1e2e1e2

    A nice thing about the geometric product is its associative so you can rewrite as e1*(e2e1)*e2… again that middle product is still just a wedge but the wedge product is anti commutative so e2e1 = -e1e2. Meaning you can rewrite the above as e1*(-e1e2)*e2 = -(e1e1)*(e2e2) = -(e1 dot e1)*(e2 dot e2) = -(1)*(1) = -1… Thus e1e2 squares to -1 and is the same as i. And now you can think of the geometric product of two vectors as uv = u dot v + u wedge v = a + bi which is just a complex number.

    In G3 you can do the same but now you have 3 basis vectors to work with, e1, e2, e3. Meaning you can construct 3 new basis bivectors e1e2, e2e3, e3e1. You can flip them to be e2e1, e3e2, e1e3 without any issues its just convention and then its the same as quaternions. They all square to -1 and e2e1*e3e2*e1e3 = -e2e1e2e3e1e3 = e2e1e2e1e3e3 = e2e1e2e1 = -1 which is the same as i,j,k of quaternions. So just like in G2 the bivectors + scalars form C you get the quaternions in G3. Both of them are just bivectors and they work the same way. Octonions and beyond can be made in higher dimensions. Geometric algebra is truly some cool shit.



  • Gnome Kat@lemmy.blahaj.zonetoScience Memes@mander.xyzteachings
    link
    fedilink
    English
    arrow-up
    5
    arrow-down
    1
    ·
    edit-2
    2 months ago

    I think you can make arbitrarily complicated roots if you move over to Gn which includes the R and C roots…

    For example the grade 4 blade (3e1e2e3e4)^2 = 9 in G4

    Complex roots are covered because the grade 2 blade (e1e2)^2 = -1 making it identical to i so Gn (n>=2) includes C.

    Gn also includes all the scalars (grade 0 blades) so all the real roots are included.

    Gn also includes all the vectors (grade 1 blades) so any vector with length 3 will square to 9 because u^2 = u dot u = |u|^2 where u is a vector.

    All blades will square to a scalar but blades are not the only thing in Gn so things get weird with the multivectors(sums of different grades). Any blade with grade n%4 < 2 will square to a positive scalar and the other grades will square to a negative, with the abs of the scalar equal to the norm2 of the blade. Can pretty much just make as many roots as you want if you are willing to move into higher dimensional spaces and use a way cooler product.



  • Gnome Kat@lemmy.blahaj.zonetoScience Memes@mander.xyzwat
    link
    fedilink
    English
    arrow-up
    8
    ·
    3 months ago

    All the people trying to explain why division and multiplication are the same and dividing by fractions bla bla bla…

    But it’s missing the point that a cell dividing is nothing like algebraic division so the analogy just doesn’t make sense.

    Saying its “dividing in half” so its actually “x/0.5 = 2x” doesn’t make any sense because the phrase “divide in half” in every other context means “x/2”…

    Any ways if you want to model a cell dividing you should use an exponential