As the above poster said, if you can introduce people to a topic by explaining a simplified or 'naive' solution/algorithm, then that could be a good springboard to learn more about the topic. Which is why there should be more comments presenting improvements and alternatives, rather than criticising what is obviously meant as a primer on optimisation. From the intro:
Gradient descent is a standard tool for optimizing complex functions iteratively within a computer program. Its goal is: given some arbitrary function, find a minima.
For some small subset of functions - those that are convex - there's just a single minima which also happens to be global. For most realistic functions, there may be many minima, so most minima are local.
Making sure the optimization finds the "best" minima and doesn't get stuck in sub-optimial minima is out of the scope of this article.
Here we'll just be dealing with the core gradient descent algorithm for finding some minima from a given starting point.
Gradient descent is neither complex nor ugly, it's the most immediate and straightforward way of searching for extrema. Iterative methods in general might be your only shot if the problem is not linear and linearisation is not an option. From a practical point of view, iterative methods in general allow you to terminate on your own terms, whereas many direct methods don't have a useful representation at hand to return prematurely.
2. Where you see fragmentation, we see diversity and a richer ecosystem. Where you see cultural disparities, we see a complex interplay of different cultures over millennia. Homogeneous populations are actually at a disadvantage because they don't have that kind of activity.
I constantly have to remind myself that people who browse HN learn strongly libertarian and are mostly well-off white males. Otherwise, saying that the US quality of life exceeds that of the UK, Germany or Switzerland is just blatantly false.
I don't see why only recent times are indicative of this. America had few outside enemies in e.g. the 1920s, and yet the inner conflicts (Teapot Dome, Steel and Railroad strikes) during those years were nothing like our recent ones.
The author is arguing precisely that the constitution should not be put on a pedestal, and that recent political deadlocks might be due to the constitution not being perfect, and not human error.
Gradient descent is a standard tool for optimizing complex functions iteratively within a computer program. Its goal is: given some arbitrary function, find a minima.
For some small subset of functions - those that are convex - there's just a single minima which also happens to be global. For most realistic functions, there may be many minima, so most minima are local.
Making sure the optimization finds the "best" minima and doesn't get stuck in sub-optimial minima is out of the scope of this article.
Here we'll just be dealing with the core gradient descent algorithm for finding some minima from a given starting point.