â–œkxrř [tired gay dragn]May 17
apocryphal mario brothers
Show threadâ–œkxrř [tired gay dragn]May 17

if we posit two functions 𝑳(x) and 𝑟(x), defined as:

𝑳(x) = 1 / x
𝑟(x) = -x

then together these two functions represent transformations of the mario vector space. if we define a mario 𝑚 to be a unit vector in this space, then we can consequently define the following, canonical brothers:

𝑳(𝑚) = 1 / 𝑚 ⇒ 𝑙 (luigi)
𝑟(𝑚) = -𝑚 ⇒ 𝑀 (wario)
𝑟(𝑳(𝑚)) = 𝑳(𝑟(𝑚)) = -1 / 𝑚 ⇒ 𝛀 (waluigi)

together these define a scalar space of finite, rational brothers.

Show threadâ–œkxrř [tired gay dragn]May 17
an important property of these transformations is that a subsequent application of the function to the output yields the original mario again -- not only are they bijective, but they are in fact their own inverses. just as luigi is the luigi of mario, so too is mario the luigi of luigi.
Show threadâ–œkxrř [tired gay dragn]May 17

we can apply these transformations to other marios to obtain some canonical variations.

for example, suppose there are some marios with a special property that we'll call "royal". we introduce a new function 𝑷(x) on the domain of marios that can produce a unique royal mario for any input mario in the domain. let's define the canonical royal mario 𝑷(𝑚) to be some princess 𝑝. using the previously defined functions, we can obtain similar results, which i've named according to my interpretation of the royal mario space

𝑳(𝑝) = 1 / 𝑝 ⇒ 𝑜 (pauline)
𝑟(𝑝) = -𝑝 ⇒ 𝑑 (daisy)
𝑟(𝑳(𝑝)) = -1 / 𝑝 ⇒ 𝑟 (rosalina)

Show threadâ–œkxrř [tired gay dragn]May 17

let's find a possible candidate for the function 𝑷(x). now, this function does not necessarily need to be bijective or its own inverse. let's choose the following definition of 𝑷(x) and explore its properties:

𝑷(x) = ln(x)

this definition gives us the following interesting identity:

𝑷(𝑳(x)) = 𝑷(1 / x) = -𝑷(x) = 𝑟(𝑷(x))

this would mean that 𝑷(𝑙) = 𝑟(𝑝), in other words, daisy is the peach of luigi. this matches the common understanding of the role of daisy in the mario calculus, though it has little grounding in traditional canon.

Show threadâ–œkxrř [tired gay dragn]
other definitions of 𝑷 may be explored that better model recent discoveries of mathematical objects that perform 𝑷-transforms, but to fully establish the properties of these objects we would first need to establish a bowsing-function 𝐁(x) in order to define a bowser 𝐵 and its corresponding bowsette 𝑷(𝐵)
May 17 at 1:07amWeb
Show threadâ–œkxrř [tired gay dragn]May 17

but we're not here to model canonical marios, we are here to invent new ones.

let's suppose the existence of an imagination function 𝑰(x) capable of producing imaginary marios. a simple definition of this function would be:

𝑰(x) = 𝑖 * x

using this definition, we can again explore some identities:

𝑰(𝑰(x)) = 𝑖 * 𝑖 * x = -x = 𝑟(x)
𝑳(𝑰(x)) = 1 / (𝑖 * x) = 𝑖 / (𝑖 * 𝑖 * x) = - 𝑖 / x = 𝑟(𝑳(𝑰(x)))

Show threadâ–œkxrř [tired gay dragn]May 17

these establish two important properties of marios in this particular imaginary space:

first, the imaginary mario 𝑰(x) is in some sense halfway between the base mario x and the wario 𝑟(x) of that mario, but in a rotational kind of halfway and not a scalar kind of halfway

second, the luigi 𝑳(x) of an imaginary mario is its own wario 𝑟(x). this suggests that imaginary marios only need to have one corresponding brother, and that brother has both luigi-like and waluigi-like properties

Show threadâ–œkxrř [tired gay dragn]May 17

now, what kind of imaginary mario could exist that is both 1) distinct from both mario and wario, but in a way where reapplying the process that obtained that mario gives you wario, and 2) has only one brother-mario with properties of both a luigi and a waluigi?

i posit: sonic the hedgehog

Show threadthe Hearth May 17
@chr something about quaternions and the whole thing with sonic, shadow, mecha sonic, and metal sonic
-F