How is a spectrum supposed to not have a total ordering? To me saying sth is a spectrum always invokes an image of being able to map to/represent the property as an interval (unbounded or bounded) which should always give it a total ordering right?
It all comes down to definitions. First off, Totally Ordered is a property of the function that compares two elements not the set you are talking about. most sets have total orderings (if the axiom of choice is true then all sets have a total ordering). With Fields and vectorspaces there is the concept of a totally ordered Field which is essentially when the total ordering is compatible with it’s field operations (e.g the set of complex numbers has many total orderings, but the field of complex numbers is not an ordered field).
So it really depends on how we define the sexuality spectrum. So long as it’s simply a set then it has a total ordering. But if we allow us to add and multiply the gays then depending on how we define those functions it could be impossible to order the gay field.
Also a total ordering doesn’t mean that there is exactly 1 maximal element (it would need to be a strict total ordering to have that property), so we can all be the gayest.
Also the definition of ‘gay’ and ‘gayest’ is poorly defined. This assumes that gay is some sort of scalar, where in reality it’s a projection from a multidimensional ‘queerspace’ that can change the appearance of the spectrum wildly depending on the methodology the one projecting uses.
Ig thats where most of my confusion comes from, to me saying sth is a “spectrum” always evokes sth along the lines of gay <--------------------> straight (ie one dimensional) with things mapping into this interval. But ig if you also include more than one axis in your meaning of “spectrum” there wouldn’t be as straight forward of an ordering for any given “spectrum”. + Like @saigot@lemmy.ca said technically even the 1 dimensional spectrum can have more than one order and the “obvious” one is just obvious because we are used to it from another context not because its specifically relevant to this situation.
Gynophilia, androphilia, romantic attraction, sexual attraction etc. absolutely makes everything complicated yeah. And then there’s cultural stuff and minor personal preferences. There’s no real end to how many axis you could legitimately argue for including in a sexuality chart.
You can impose a partial ordering on it. HSL uses a hue angle. If we assume full saturation and lightness and pick an arbitrary direction to be positive, there’s your partial ordering. But not total ordering, there is no most clockwise color.
I feel like this doesn’t qualify as an ordering relationship, because of the circular nature of the wheel: for any two elements a and b (a ≠ b) on the wheel it’s both true that a is further clockwise than b and b is further clockwise than a (just keep rotating). This violates the antisymmetry property that an ordering relation should have.
You can fix it by establishing some point on the wheel as “least clockwise” (essentially unfolding it into just a straight line) but that immediately establishes a total ordering.
How is a spectrum supposed to not have a total ordering? To me saying sth is a spectrum always invokes an image of being able to map to/represent the property as an interval (unbounded or bounded) which should always give it a total ordering right?
It all comes down to definitions. First off, Totally Ordered is a property of the function that compares two elements not the set you are talking about. most sets have total orderings (if the axiom of choice is true then all sets have a total ordering). With Fields and vectorspaces there is the concept of a totally ordered Field which is essentially when the total ordering is compatible with it’s field operations (e.g the set of complex numbers has many total orderings, but the field of complex numbers is not an ordered field).
So it really depends on how we define the sexuality spectrum. So long as it’s simply a set then it has a total ordering. But if we allow us to add and multiply the gays then depending on how we define those functions it could be impossible to order the gay field.
Also a total ordering doesn’t mean that there is exactly 1 maximal element (it would need to be a strict total ordering to have that property), so we can all be the gayest.
Gay field… A word I never imagined will encounter in my life
Also the definition of ‘gay’ and ‘gayest’ is poorly defined. This assumes that gay is some sort of scalar, where in reality it’s a projection from a multidimensional ‘queerspace’ that can change the appearance of the spectrum wildly depending on the methodology the one projecting uses.
A spectrum can have multiple dimensions, but that might not matter if you’re only comparing in a single dimension?
Ig thats where most of my confusion comes from, to me saying sth is a “spectrum” always evokes sth along the lines of
gay <--------------------> straight(ie one dimensional) with things mapping into this interval. But ig if you also include more than one axis in your meaning of “spectrum” there wouldn’t be as straight forward of an ordering for any given “spectrum”. + Like @saigot@lemmy.ca said technically even the 1 dimensional spectrum can have more than one order and the “obvious” one is just obvious because we are used to it from another context not because its specifically relevant to this situation.Gynophilia, androphilia, romantic attraction, sexual attraction etc. absolutely makes everything complicated yeah. And then there’s cultural stuff and minor personal preferences. There’s no real end to how many axis you could legitimately argue for including in a sexuality chart.
The color wheel, for instance
A colour wheel is not even partially ordered, I don’t think. There is a relation between some colours on the wheel but it’s not an ordering.
You can impose a partial ordering on it. HSL uses a hue angle. If we assume full saturation and lightness and pick an arbitrary direction to be positive, there’s your partial ordering. But not total ordering, there is no most clockwise color.
I feel like this doesn’t qualify as an ordering relationship, because of the circular nature of the wheel: for any two elements a and b (a ≠ b) on the wheel it’s both true that a is further clockwise than b and b is further clockwise than a (just keep rotating). This violates the antisymmetry property that an ordering relation should have.
You can fix it by establishing some point on the wheel as “least clockwise” (essentially unfolding it into just a straight line) but that immediately establishes a total ordering.
Measure acute only. Idk how to deal with 180° though