2023-08-28

maths 4

square

<-- previously

line


for a line, all that's needed is x

and x marks the spot

it doesn't really matter which direction the line is going

it could be a line on a piece of paper

it could be the line between where you are sitting and the closest satellite

it's a line and it has the length dimension

lines are 1D and if it starts at zero then its length is x

an x ordinate, i guess.

it is when x teams up with y that it is a 'co-ordinate', right

cube

zero is where x meets y

whatever that means. the x line and the y line must be invisible. no thickness.

my goodness, how can zero exist?

yeah it's an infinitely smol point. it doesn't really exist.

but like time, nothing exists without it

head flosses

we have a fishing line for x and a fishing line for y

x is horizontal and y is vertical and they are perpendicularrr

you know the thing.. it's just a model.. and we need it for 2D shapes, baby

plane

The Plane

let's put our head at zero

imagine putting your head at the centre of the plane

and the fishing line of x is going through your ears

the y line going straight through the top of your dome

your ears are level with zero, the line going perfectly straight through

you move your head slowly left, ears remaining level

the line rubs against the insides of your nose and the back of your eyes as it glides through your brain. your eyes and nose have entered the negative number zone, left of zero.

now, come back to the right, and slide your head past zero. go to about 2.3

then slowly back to -2.3, hold it there a second, and then go right to 2.3

repeat this left-and-right flossing your head, for about 5 minutes

you see? you didn't need to keep your ears level.

you can tilt your head the next time you floss, if it is more comfortable.

the lines just need to be perpendicularrr

imagine a protractorrr
start the propellerrr
rrroll your arrrs

the dual vibrations help with flossing, similarly to an electric toothbrush

shake that dementia dust off of your pineal gland

x and y

x feels easier than y

can we do a vertical floss? sure. get in those nooks, crannies, and other angles.

you move your head slowly down below zero. and then up above zero.

imagine as your head moves up and down, that the x line, that is going through your ears, is moving up and down as well. where the x line meets the y line is the spot. the value of y.

when we floss left and right, the y line comes along, and measures the x value.

if we move in any diagonal, both lines continue to move with our head.

the centre of our head is the spot, measuring the x and y values.

let's put the spot back on zero and get our head back.

just in time to get shot through the eyes with z

cube

x y z

pop will north-east itself

now we can move our head anywhere!

we can walk, do cartwheels, climb a mountain..

our head marks the x, y, z values from zero..

wherever zero is

do x, y, z determine zero, or does zero determine them..

anyway, wherever we go in 3D, our head marks the spot with the three lines..

a line from zero, a length dimension, in any direction, to where your head at

this most direct line

the 4th line going through your head

lines

one more..

imagine that zero has three lines going through it

it has three lines and your head has three lines

i come by and there's lines going through my head too

if i put my head at zero, my lines line up with zero's lines, aligned

moving away from zero in a line..

splits the sets of three lines because of moving on the fourth line

time is moving