orlp

@RoddyMacPhee oh hey, sorry, just came here from a recommended meta question don't really have anything to add to the discussion

I'm just saying that someone should make some challenge of it

there's many ideas to go off :P

@EriktheOutgolfer no idea

someone make this into a challenge

then set it equal to 0 and solve

wait maybe I can differentiate the variance with respect to c

alright yeah, then continue

ohh

note the ti on the last line

yes

they all sum to t[x] which is not linear (but if we wrap the sum in ti it will obviously sum to x)

to make it easy to debug I wrap the entire sum in a ti

no

they're probabilities

the bumps are only a visualization though

@flawr I am sort of, a linear combination of basis vectors can make any other vector

and I have no idea if it's even close to optimal

it has a small kink

but no mathematical justification

it's definitely workable

this is what I got from manually fitting a curve

imgur.com/a/TZMXxv3

meaning I only have to find x

giving me y, z in terms of x

leaving out the constant variance

has been to solve the above system of equations under-determined

my best result so far

I don't know what a basis function is

so we need non-constant variance but I have no idea what/how

and I've tried various (hehe) constant variances but they all are broken

since the solution is unique (3 variables, 3 equations) and it doesn't work we know that we can't have constant 1/4 variance

but the probabilities aren't in [0, 1]

and the average does come to c

the variance is 1/4

yes, the probabilities sum to 1

it's not correct

@flawr unfortunately the result is a total mess

that was the next logical step

@flawr i.imgur.com/D6IRQiy.png

and their variances to the y = 1/4 curve

it really is quite magic that these curves perfectly add up to the y = x curve :D

we just have 3 functions in the neighbourhood of any c

because instead of having to solve integration

this way simplifies the problem immensely

and c = 3 has the highest chance of quantizing to 3

but c = 4 has a small chance of quantizing to 3