And this math is kind of a mess. exp(x) is its own derivative but the log is not. (d/dx)log(x) = 1/x
But, agreed, if you're going to do calculus, use radians.
The derivative of log_b x is 1/(x ln b), where ln b is 1 if b is e.
The computational aspect of it is totally compelling. The library routines are already using turns internally, so it is wasteful to go from/to radians when the caller doesn't require it, and many callers can be rewritten not to. Plus the part argument about common angles like multiples of the right angle having to be irrational numbers under radians is also compelling.
Assume people have read the article and understood it.
If your code doesn't look like the math it's "ported" from, the odds of it being bad code go up like 100x
It's important to note that such cases are not always clearly signaled as being humor or untrue. It is a part of the joke's effect that the reader or listener will not at first know it is a joke, but will realize it after noticing an absurdity.
A related concept is "dry humor".
And for all the people who are concerned about how sin' 2πx = 2π cos 2πx, in actual code, it doesn’t matter. Let’s say that I’m writing a basic graphing function and I want to be able to display the slope of the sin curve at any point.
I am not going to expose the turn-based units to the user. Caring about slopes implies that I’m doing calculus and thus assuming radians. So even though my internal values are [0,1], I will label them as [0, 2π] (and the actual numeric values on the display may actually be something like [50,450] which is yet another numeric value we don’t display). So to get the slope at π/4, I’ll calculate cos_t 0.125 and display that value.
We do all kinds of unit translations in computing without worrying about it. This is just another case of that which observes that numerically speaking, using turns is better aligned with the underlying numerical algorithm for calculating trig values.
Haha !
I have been coding for much shorter time but having done some ML on orientations and on spheres in my time, I have had to take their derivatives all the time.
It will be interesting to consider folks who do machine learning on robot trajectories or analysing dynamics of robotic arms.
You could be using the results of calculus, which became frazzled with gratuitous constants because of poor angle units before anyone wrote any code.
You want to keep all the math in radians until you code the calculations; then figure out how to optimize it with turns where possible.
It sounds like discussions about "porting from math" do not pertain to you then?