clockwise

i've been one to have my fascinations and obsessions with taxonomy and labeling, and that can vary between serious and unserious,
but one thing that i felt was particularly egregious was the lack of labels for the two chiralities of 2-dimensional spiral. i was
first alerted to this issue one day when trying to purchase a honey-bun from a vending machine at my job. it's crazy to me, by the
way, that an office i work for would charge me for snacks. i guess since they're provided by an outside vendor but like. man.

anyway the issue- well let me explain how the vending machine normally works: snacks rest on helical coils, some on only one
coil, some requiring two coils to support them. each coil is alternating in chirality, and when the machine needs to dispense
a treat, it rotates the coil in the direction that causes the shape of the coil to push the snack forth and drop into the uhh
retrieval zone? anyway the issue was that when you tried to order the honeybun it was getting pulled deeper into the machine
instead of being pushed outward - after studying it closer i noticed that the two coils its slot used were in reverse order.
the same mechanical movement that would have worked didnt because of the chiralities of the helixes involved were inverted.

at the time i really didnt understand the helixes but it made me think of spirals and their two chiralities, which i tried to come
up with fitting names for with group help. essentially, the difference between the two is that for one, following the spiral inwards
has you trace clockwise, whereas tracing the other *outwards* is clockwise. now you might be tempted to call them "inward" and
"outward" spirals, but that hinges on defining them based on which way is clockwise, so if you're trying to remember which is
which you have to remember an arbitrary detail. i'm picky and i want the names to be inherently descriptive.

(Helixes have a defined name for their two chiralities and it's bad for both reasons - they're called "left handed" and "right handed",
which is incredibly indescriptive, and they apparently are describing the direction based on a specific motion that would be done
with your hand which like... how would anyone know that from the name? and then having to remember what motion is like, its just so bad.)

Unfortunately, something like "in clockwise, out counterclockwise spiral" and "out clockwise, in counterclockwise spiral" is too
too too long. Much like the helixes a term like right/left handed came to mind but i quickly discovered the issue when nobody could
agree on which would be which. the next idea was the e and G spirals, whose names (e and G) visually resembled the spirals themselves.

This wasn't terrible, but currently I'm championing J spiral and L spiral as names - named after the tetrominos that most minimally
give the impression of their shape on a square grid. Take a look:

###### ###### (i recommend a monospace font)
# #
###J # # L###
# J # # L #
# JJ # # LL #
# # # #
###### ######

This minimalism is very satisfying to me. It also lends itself to naming the degenerate spiral (a circle) an O spiral, which makes sense as O is
a closed loop tetromino, and an O is a circle. You can also name the two doubled up versions of those spirals after two more tetrominos, S and Z:

######### ######### (there isn't much to show
# # for the O spiral)
# ####### ####### #
# # # # # #
# # SS# # # #ZZ # #
# #SS # # # # ZZ# #
# # # # # #
####### # # #######
# #
######### #########

if you want to fill out the rest of the tetrominos, you need to reckon with I and T which are... troublesome here

####IIII####

I appears to be... a straight line. someone suggested that this would be a spiral with no curveature? sure

TTT
T

but i dont even know where to begin with T

going off on a tangent about spirals and chirality and the like, today i found myself thinking about the different directions i turn keys in locks,
as it had come up in conversation a month or so before. i tried to take note of which direction i turned each key to open and close everything,
then the handle on the door, and then stopped when i realized i don't know which direction the door opens.

more specifically it occurred to me that it was only defined relative to the position of the observer - clockwise becomes counterclockwise when viewed from the back side.
this doesn't apply to helixes, but of course if you rotate them in like 4d or whatever theyre the same thing. probably.

it got me thinking about measurement, and the fact that every measurement we have is relative. our rotations are relative, even the fancy 3d ones, pitch, roll, and yaw, are relative to the earth's surface. an inch is an inch only as close as we can replicate the original inch. the official kilogram loses part of it's weight through gradual erosion. all recordings are just the interpretations of the vibrating echoes of what there is, tracing out the shape as best as they can

i immediately took comfort back in mathematics. 1 + 1 is always 2, and that is a platonic ideal. if there are 3 coplanar but noncolinear points in space, they form what is called a triangle, and if the angles at which rays cast from these triangles intersecting each other points forms a right triangle, the distance between the furthest two points is equal to the square root of the distance of the sum of the squares of the distances of the other two pairs of points from eachother.

...in euclidean space, that is. really, only by definition. i remembered the time i searched for a reason why pi was the value it was and why the euclidean metric led to weird irrational values, why the total distance of a vertical and horizontal movement together was the square root of their squares summed instead of just, like, adding them as in the taxicab metric. i found some articles showing that the value for pi in different metrics defined similarly to ours and the taxicab metric varied between as high as infinity and dropping all the way down to 4, but not before stopping at pi, the global minimum of the curve of values.

this weird irrational transcendental number, at the bottom of a formula i couldnt wrap my head around. i tried reading more into it and playing with it in desmos but it was above my mathematics level.

i take comfort in knowing that pi is at the extreme of some presumably logical function, and not just a value plucked from the aether as a result of some arbitrary choice, as were in contrast the values and units i spent my time dealing with (the value of a dollar, the weight and mass of objects, etc), but i'm still not satisfied in my understanding

i dont want to categorize everything, i dont want to taxonomize everything, i just want one thing i can know to be exact and true. maybe i should start meditating on the reflexive property. i've yet to meet an algebra or logic that doesn't adopt it.

#math #futile #algebra #spiral