alex @alexthecamel@schelling.pt

like i kid you not it is

the claim seems to be that the fact that n-TET is a good tuning corresponds to
zeta(1/2 + 2*pi*n*i/ln(2)) has a peak in absolute value

someone stop the avant garde musicians
they are out of control
https://en.xen.wiki/w/The_Riemann_zeta_function_and_tuning

apparently in music theory people use "irrational time signature" to mean "non-dyadic time signature" :/

i feel like you could do something actually interesting with say a time signature based on the golden ratio but you have ruined my ability to see if it's been tried

ppl make the same mistakes teaching autists social skills as they do teaching normies math

as always my take on the transmed/tucute discourse i.e. "is being trans about having a mental illness called gender dyphoria"
is that if this is a meaningful question for you y'all need to get woker about disability rights activism

i feel like you can repeat the argument in full generality with some bespoke metric on the space of all tilings where the tiles are allowed to slide around but that seems like effort

you feel like there has to be a one-line proof citing some theorem in model theory or something

(in actuality S_α will become constant while α is still countable
because our basis is countable
and the set of things B_α in our basis which are a subset of the open set S\S_ α always gets bigger as α goes up
and as S\S_α is the union of all things in B_α...)

and one point in this space always gives you an infinite number because aperiodic

i think this reasoning still works if we're talking tiles where there's only a finite number of ways to glue 2 tiles together sensibly
you don't quite get the group action but you do still get a compact topology on all the ways to build a tesselation around some base tile

S_α is also eventually constant if for no other reason than that eventually you run out of points. call the resulting set T

pretty sure because T is perfect and this is a nice enough topological space T has cardinality continuum

S_α is always closed, nonempty, and infinite

hrmm. construct for any ordinal α S_α

S_0=S
S_{α+1} is S_α minus all its isolated points

S_λ is the intersection of S_α α<λ

like the space S of aperiodic tilings comes with a compact topology where the basis of open sets is "we are given where a finite number of where the tiles are is"
and Z^2 acts freely on this set by translations because the tiling is aperiodic

(note this reasoning does not hold if there exists a periodic tiling, and I feel like it's not too difficult to construct counterexamples here)

and one point in this space always gives you an infinite number because aperiodic

i think this reasoning still works if we're talking tiles where there's only a finite number of ways to glue 2 tiles together sensibly
you don't quite get the group action but you do still get a compact topology on all the ways to build a tesselation around some base tile

S_α is also eventually constant if for no other reason than that eventually you run out of points. call the resulting set T

pretty sure because T is perfect and this is a nice enough topological space T has cardinality continuum

S_α is always closed, nonempty, and infinite