Bumby the Loaf @wallhackio@cat.family

@cam OH SHIT

when i watched lucy play the Don't Stop, Girlypop in efdn vc that one time the best parts of the game were the Yeehaw Tamagotchi and this song: https://www.youtube.com/watch?v=GLgnurE4BRI

@vaporeon_ the formatting here is all fucked up. Too bad!

@sudo_EatPant friend, reported for suggesting otherwise

@vaporeon_ @vaporeon_ in physics you learn about vectors. we are told that vectors are the language of physics. in your very first semester of college (and likely high school physics) you learn about vectors. and yet vectors were only formalized in the early 1900s! what did physics even look like before vectors?

I haven't fully answered this question for myself but an important part of the history is the concept of the "quaternion". The famous Irish mathematician William Rowan Hamilton wanted to extend numbers to three dimensions. Of course, complex numbers can be understood as a "two-dimensional" analogue to numbers since you can plot the real and complex part of a number on a two dimensional plane. We write a complex number like x + iy. You might think that to extend numbers to three dimensions you would make a "super complex" number, something like x + iy + jz

However, Hamilton wanted numbers that exhibited all of the properties exhibited by real and complex numbers. Things like inverses, in which I can multiply a number by another number, and then divide by that same number to get the original number. He couldn't find a way to do this with numbers of the form x + iy + jz

The trick Hamilton came up with was to create numbers in four parts to represent three dimensions. That is, numbers were of the form a + bi + cj + dk. He called these numbers quarternions. The numbers associated with the i, j, and k were parts of three dimensions, and the extra number not associated with an i, j, and k was an auxiliary piece of the number that helped give the structure desirable mathematical properties. With this structure he was able to define multiplication is a way that created inverses! (Fascinatingly, a mathematician later proved that real numbers, complex numbers, and quaternions were the only numbers that could possibly satisfy all of the algebraic properties Hamilton was looking for!! No other mathematical structure was capable of having all of these properties! Hamilton was unknowingly looking for extremely privileged information!!!!)

When we multiply quaternions, we multiply them using the distributive rules of ordinary algebra:

(a + i*b + *j*c + *k*d) * (e + *i*f + *j*g + *k*h)
= ae + *i*af + *j*ag + *k*ah +
*i*be + *ii*bf + *ij*bg + *ik*bh +
*j*ce + *ji*bf + *jj*cg + *jk*ch +
*k*de + *ki*df + *kj*dg + *k*k*dh

To simplify further Hamilton introduced the following rules for the multiplication of i, j, and k with each other:

ii* = *jj* = kk = -1
ij = k
jk = i
ki = j

ji = -k
kj = -i
ik = -j

With these rules the multiplication of two quaternions simplifies to

(a + *i*b + *j*c + *k*d) * (e + *i*f + *j*g + *k*h)

= ae + i*af + *j*ag + *k*ah +
*i*be + *ii*bf + *ij*bg + *ik*bh +
*j*ce + *ji*bf + *jj*cg + *jk*ch +
*k*de + *ki*df + *kj*dg + *k*k*dh

= ae + *i*af + *j*ag + *k*ah +
*i*be - bf + *k*bg - *j*bh +
*j*ce - *k*bf - cg + *i*ch +
*k*de + *j*df - *i*dg - dh

= (ae - dh - cg - bf) + i(af + be + ch - dg) + j(ag - bh + ce + df) + k(ah + bg - bf + de)

Okay, so what? Well, let's consider the specific case where we multiply two numbers which only have nonzero parts in the i, j, and k parts. That is, a=e=0. The result is

(i*b + *j*c + *k*d) * (*i*f + *j*g + *k*h)
= -(dh - cg - bf) + *i(ch - dg) + j(-bh + df) + k(bg - cf)

Well hold on. The part without i, j and k looks like the negative of the dot product:

(*i*b + *j*c + *k*d) * (*i*f + *j*g + *k*h) = (dh - cg - bf)

And the part with i, j, and k looks like the cross product!!!

(i*b + *j*c + *k*d) ❌ (*i*f + *j*g + *k*h)
= *i(ch - dg) + j(-bh + df) + k(bg - cf)

It ends up that these two parts of quaternions were often useful in practical calculations, and the creation of vectors, the dot product, and the cross product resulted in the recognition of the usefulness of these two parts of quarternions!!!!!!

@baronvonjace i forgor i was too drunk at the time 💀

@coriander the softest goblin!!!!

@aschmitz it was a great time I love my roommates dad (who is the neighbor in question)

also he and his wife fed me lots of good food once they realized I was plastered

@The_T

@baronvonjace my roommates dad wanted to make me a martini and then I drank it and because it was a wet martini he gave me a dry martini and then his wife made a white lady she didn't like and then offered it to me and I was on an empty stomach at the time

@The_T I would but I'm broke sorry The T

@aschmitz my neighbor wanted to make me a martini and because I tried a wet martini he also made me a dry martini but then his wife made a white lady that she didn't like so she offered it to me and I was on an empty stomach and I drank it all

@vaporeon_ give me a second I'll make a somewhat long write up in a sec

I am very drunk ama

@amy oh some narrator from jackbox

@amy who is cookie mastodon

I had a character with an axe that had a 67% chance of hitting and would strike twice (each hit has the 67% hit probability). I had three turns to hit a character before they escaped with a valuable item. It would take two hits to defeat this enemy.

Now, Fire Emblem 3 Houses lies with its % reporting. Percentages above 50% are actually higher than reported and percentages lower than 50% are lower than reported. Without going into too much detail, a reported 67% hit chance is actually 78.55%.

So, to not defeat the enemy in time, I needed every attack to miss or five of the attacks to miss. The probability for every attack missing is

1) (1 - 0.7855)⁶

If we have a 78.55% chance to hit then we have a 100% - 78.55% to miss. We multiply this probability for each miss.

Meanwhile, the probability for five misses and one hits is
2) 6 * (0.7855)¹ * (1 - 0.7855)⁵

We have the probability of missing five times and the probability of hitting once. Now, why the multiplicative factor of six? That's because the single attack that hits could be the first, second, third, fourth, fifth, or sixth swing, and we must account for every case.

The total probability of not defeating the enemy is the sum of the two cases.

(1 - 0.7855)⁶ + 6 * (0.7855)¹ * (1 - 0.7855)⁵ = 0.00223750036

which is about a 0.22% chance. The probability of defeating the enemy was 0.99776249963 or about a 99.776% chance. Fuck me

I did something that had a 99.776% chance of working and it failed fuck this chungus earth