Should we appreciate art we were manipulated into liking, or pretending to appreciate?
Modern art has been the butt of many jokes over the years. A canvas painted white, a banana duck taped to a wall, literal piles of trash… the bar for what we call art is basically on the floor. A literal bar on the floor, given a good story, could itself be called art.
Art generally implies some level of skill. While some modern art can still fall into that category, other stuff requires no real skill, just the right connections and for enough people to buy into the grift.
I love art. Contemporary art is a bunch of ugly wankery by pretentious people who are bored of actual beauty and can only amuse themselves by creating ugly stuff, then claiming "you just don't get it". The world would be a significantly better place without contemporary art in it.
If there is any change I could make to the human personality at large it would be the reflexive opinion that anything you don't understand, or even dislike, is automatically morally wrong.
This might shock you, but most art is made by artists. Artists also tend to spend lots of their time consuming other art. This informs the type of art they create.
Here's an anecdote: Pablo Picasso learned to paint realistic scenes, including humans, the equivalent of Da Vinci or Michelangelo, around the age of 17 or 18.
Where do you go from there? In his case, he went towards cubism and other such "modern art". Why do you suppose that is?
It's because both radians and degrees are are a ratio of a length to another length and are thus dimensionless. No matter how you measure it, all angles are without a unit.
It's most obvious with radians but it's also the case with degrees.
Using radians, you are guaranteed to not introduce unusual extra terms to rescale angles, if you use any other scale of angle you will have to keep track of extra terms.
That may be useful in whatever you're doing. I work in degrees quite often and I'm careful to keep track of the 2pi/360 terms that crop up all over the place. With grade measure you have to keep track of 2pi/400 terms and with turns you have to keep track of 2pi/1 terms that will repeatedly show up.
Again, depending on what you're doing, this may or may not make sense to do.
In general, mathematics works out easier when the scaling term is 2pi/2pi because then you have a lovely 1 scale factor you don't have to keep track of.
It is dimensionless by fiat and convention. It clearly has units such as degrees, grad and radians. Just like other quantities that have units, a specific measurement is expressed as a pure numerical multiple of an unit which may be radians, degrees etc.
This is a known wrinkle in dimensional analysis and people have considered making angles a fundamental quantity such as mass, length and time but have not done so because of the disruption it would cause.
> The current state of affairs leads inevitably to ghostly appearances and disappearances of the radian in the dimensional analysis of physical equations.
In "A spectral unit", Nature Physics (2020) - https://www.nature.com/articles/s41567-020-0997-3.pdf Giacomo Prando summarizes the troubled history of the radian, a unit with the odd property of appearing and disappearing seemingly at will in dimensional formulas
It led me to reading about "dimensionless quantity".
> There have been periodic proposals to "patch" the SI system to reduce confusion regarding physical dimensions. For example, a 2017 op-ed in Nature argued for formalizing the radian as a physical unit.
> The idea was rebutted on the grounds that such a change would raise inconsistencies for both established dimensionless groups, like the Strouhal number, and for mathematically distinct entities that happen to have the same units, like torque (a vector product) versus energy (a scalar product).
What's surprising is that these discussions are so recent, considering the wide implications on so much practical work in mechanics and engineering. Maybe people got so used to working around the question, that any proposed solution would be too disruptive - so it's better to keep things backward compatible rather than conceptually simple/clear and explicit.
In another comment someone said, "types" (in programming and type theory, I'd guess) are a poor model of physics units. But I wonder about that, it seems "units" are something like types with associated quantities, like degrees with 360, or meters with the speed of light.
Certainly pi (and e) must be one of those fundamental constants regardless of any unit of measurement. A "turn", on the other hand - well, if we consider 1 as a dimensionless constant that means a "whole"..
Ensuring units agree is indeed a form of type checking. A more thorough procedure for the former is dimensional analysis.
I think the fact that action and angular momentum have the same units played an illuminating role in making sense in Bohr's model regarding why only certain orbits are allowed.
Not sure how that would play out once angle is considered a fundamental entity.
In another comment I made in this thread https://news.ycombinator.com/item?id=49373317 I think it came to the understanding that a "turn" is similar to a dimensionless quantity, as it takes the full circle/cycle as a fundamental 1. Apparently, using the turn as a unit allows one to get rid of pi and e in Euler's formula in favor of 1 and -1.
You might find the following interesting. It is about trigonometry as practiced by early Indian mathematicians. Rather than using an unit circle they used a circle of 3438 units.
Dimensions and units are separate things, though. For example, 1 minute and 1 second are different units of the same time dimension. Similarly, 1 rad and 1 degree are both dimensionless, but they are both different units.
Theoretically, you can define systems of measurement where a lot of seemingly separate things fall on the same units and dimensions. There are "natural units" in physics where you take the fundamental nature of particles and relativity into account and make some convenient choices for some physical constants such as the speed of light c := 1. Then the speed becomes dimensionless, length and time have the same unit and dimension (a length of 1eV is a time period of 1eV), and almost all units are simply derived from a measurement of energy (electron volt, not as basic as people would like, but useful enough).
> Then the speed becomes dimensionless, length and time have the same unit and dimension
Uh, that is not what the article you linked is saying. Natural units don’t make speed dimensionless, nor allow you to use the same unit for length and time. Natural units remove the conversion constants, not the units or dimensions.
Perhaps in the physics sense, but in computer science we do have the notion of types which does allow us to model the difference between an angle and other numerics.
