Gnome Kat

That’s low key the charm of it. I use to only use reddit and it confused me too at first. I never used Twitter but on mastodon you can actually make friends with people. Friends who will discuss the topics you are interested in. I have queer friends on there and gamedev friend and math friends. We are interested in the same things, we boost posts that we all are interested in. Make general often vague looking posts because we know who will see it, like a long drawn out conversation. Its so much cozier than lemmy or reddit, here everyone is trying to correct each other or yell at each other or be the cleverest comment in the thread. On mastodon people are alot more interested in being authentic, thats been my experience of mastodon at least.

mastodon is fantastic and is honestly better than lemmy community wise.

not gay, not trans… not even vegetarian.

how unfortunate

When you’re accustomed to privilege equality feels like oppression.

Its the algebraic properties that are important, not all vectors are n-tuples, eg the set of polynomials of degree less than n.

You need a basis to coordinate a vector, you can work with vectors without doing that and just deal with the algebraic properties. The coordinate representation is dependent on the basis chosen and isn’t fundamental to the vector. So calling them n-tuples isn’t technically correct.

You can turn them into a set of coordinates if you have a basis, but the fact that you can do that is because of the algebraic properties so it’s those properties which define what a vector is.

It should be magnitude plus orientation, not velocity. Velocity itself is a vector quantity

I think the definition of consciousness needs to not be solely about abilities or attributes. It needs to account for the active process of consciousness. Like a hair dryer can burn things… but a fire is things burning. Without the active nature its simply not conscious.

Just FYI content warning for Pantheon there is a seriously disturbing gore/kill scene that is animated too well in the first season. Anyone who has seen the show knows what scene I am talking about, I found the scene pretty upsetting and I almost didn’t finish the show. I am still a little upset that the scene is burned in my memory.

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.

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.

Flipwitch: Forbidden Sex Hex :D

Very horny and actually pretty decent metroidvania, lots of jiggly titties

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

I am also always immensely confused how gamers don’t see valve taking 30% of pc sales and not recognize that as greedy shit bag behavior.

We all know when google or apple does it on their app store its bad, or when spotify pays artists pennies its bad, or when actors are striking because of its shady residuals payout from streaming its bad. But when king gaben does it, its fine perfectly ok. Even though game devs are some of the most overworked and underpaid workers in tech. And then people wonder why games suck lately.

a caffeine pill…

Im wearing a Kirby shirt rn (⁠.⁠ ⁠❛⁠ ⁠ᴗ⁠ ⁠❛⁠.⁠)

Putting things in base 10 is also a definition. Digits aren’t special.

one thing that might need fixing is the alternative interface does not display the correct fav icon

this is fantastic… absolutely love alexandrite

I just think its bad cus it supports transphobia…

but with a core dump you can just load it up and see the state of the process when it crashed…