I think there is a reconciliation. If you read the other article popular today (https://news.ycombinator.com/item?id=37493955 https://news.ycombinator.com/item

I think there is a reconciliation. If you read the other article popular today (https://news.ycombinator.com/item?id=37493955 https://news.ycombinator.com/item?id=37493955), it focuses on scale invariance as the driving principle and gives an example of units for Fourier coefficients. I think one subtle aspect here not really covered in that other article is sort of a "duality" between "scale invariance" and "carrying scale tags" along with expressions. This also happens in differential geometry or even just analytic geometry / vectors where you can often either use an abstract geometric object notation or carry along index subscripts. So, you can think of it units as carrying along scales you care to track "for whatever reason". The most common reason for physical units is varying conventions/devices to measure something. Angle measurers care about their own devices and so their units. By carrying along the scale you make the number a surrogate for a hypothetical experimental result. Unit conversion can be seen as how to translate from one (kind of) apparatus to another. So, while args to trig functions are dimensionless, you do not have to be as strict about angles. You could retain them and make people carry along a multiplicative factor inside the parameters which is likely what people with instruments measuring angles in non-radians do. Similarly, you could also (probably coherently though I have not thought deeply about it) expand SI to 8 base units adding "axial-meters". The number of base units / scales to carry along is arbitrary. It just depends upon how much expressional error checking is desired as @contravariant observes. (system conversion has its own structure as per my other comment elsethread, unelaborated by both articles.) Because the "axialness" factor is more "kind than amount" (and binary at that), besides contravariant's (probably better) angle-dimension idea, it might be more like how `i=sqrt(-1)` creates a 2nd dimension for real numbers and you carry along that factor to make the complex plane. I have no idea how popular this kind of "complex length unit" would be in terms of error catching value for its carrying-along cost, though.