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.
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.
There was a time when Germany used to be the leading country in the world where almost all major thoughts and works were produced. Whether it was Literature, Art, Philosophy, Cinema, political thinking, Germany was the place to go (and because of close interactions, Austria).
Before that, it was Arab World, before that Ancient Rome, before than Ancient Greece.
Today that status belongs to America. If you want to produce anything which would make impact in the world, the most fertile ground for that is America. Even if a talent rises up say in Germany, the network effect of America attracts those individual to come to America. Maybe there is a smarter Elon Musk in South Africa, but the main point is that Elon Musk never came to America, this Elon Musk did.
I am not saying that somehow by being in America you automatically will be more likely to produce great thinking. Rather its more like being among more challenging and talented peers will bring your exposure and contribution to another level, something which isn't possible currently (even with the Internet) to be in Germany or Switzerland.
Just so I get this straight, you are claiming that America currently is the go to place for literature, art, philosophy, cinema and political thinking?
I'd accept such a claim for web scale technology and some other fields but for all of the above definitely not so much.
I missed technology and science in my list of things, but yeah that too.
If we use Nobel prizes as a metric, then US beats other countries by a wide margin in everything except Literature. (Surprisingly Germany and UK, the old world leaders still come close second, but then we ARE considering nobel prizes awarded between 1901-2014). In terms of per capita, US is ranked 19th, and UK, the only large country in terms of population ranks higher.
It's true that USA is world's third largest populous country, so in terms of absolute numbers it beats other nations hands down, but there are two things which need to be considered. If EU was a single nation with single language and no immigration restrictions, then you will get the same benefit of being in EU(400+ Nobel prizes) as much as you'd get of being in America(350+ nobel prizes), that is, more integrated intellectual networks. But EU is fragmented into different nations, and despite of being an open border, the linguistic and cultural disparities do fragment the number of people you could have been connected to.
Second point is, almost all major figures in art and literature in America have lived in NYC at some point or the other. This usually means that if you lived in NYC, there are future nobel laureates living here with whom you might be interacting. So I think that not only you need to be in America in order to access the biggest network effect of anything, you need to be in one of the larger cities like NYC or SF.
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 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.
Maybe I should put it this way: US already reached its peak status, and it's very difficult to even find a way or area to "grow". In 1920s, although US became an economic super power, there were still plenty of room to grow in the area of international political system.
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.
The fallacy here is that deadlocks are a bad thing, usually they are not. You don't want a slim majority being able to drive the government at a breakneck pace. When society is deadlocked, government should be too. You want action only when there is fairly broad agreement.
Exactly. While I'm sure they didn't mean "deadlock", delay was precisely what the framers had in mind. The emphasis on super-majorities and agreement between multiple bodies was designed to keep mob mentality from fundamentally changing the people's rights in the heat of the moment.
I'd argue this has eroded in recent decades due to lack of transparency, which has greatly hindered the third branch, the Judiciary, from being able to act as effectively as it might have otherwise.
> which has greatly hindered the third branch, the Judiciary, from being able to act as effectively as it might have otherwise.
I don't think that the American judiciary's problem is that it's hindered in its actions.
Historically, we should have seen more impeachments of federal officials; Congress needs to wield its authority in an exercise of checks and balances on the executive and judicial branches.
Well, the idea of Congress impeaching judges frankly terrifies me, and given that Congress holds up most executive appointments as it is, I'm not sure they could do much more damage there.
The Ethics Committees largely hand-slap only the most gross violations of their members. I see your intent there, but I'd much rather see Congress holding a higher standard of itself.
If you're referring to the overreach of Federal officials, then that gets a bit more sticky. Yes, it should be reined in, but when I see one Congressmen one-upping another on how we need to be "tough" or have "no tolerance" for this or that, I'm little surprised that our police and intelligence agencies act the way they do.
> when I see one Congressmen one-upping another on how we need to be "tough" or have "no tolerance" for this or that, I'm little surprised that our police and intelligence agencies act the way they do.
Puritanism dies hard. I'd say the constitution is working perfectly: the government we have is the one we deserve and one that really does reflect what this country, on the whole, wants. People in this country are still overall prudes who want harsh punishments, and that's what we've got. We don't need to fix the constitution, because that won't fix the root cause which is that our society needs fixing.
>I'd say the constitution is working perfectly: the government we have is the one we deserve and one that really does reflect what this country, on the whole, wants.
Can you justify this in a non-self-referential way, ie: via data other than election outcomes?
I'd agree with that if we had Congressional term limits to make Congress more answerable to the people. As it is, incumbency is way too powerful and is partly to blame for the dysfunction we're currently seeing.
At the end of the day, I think that making government more accountable to its people is more directly established by migrating more power to the states, and away from the federal government.
I have a much greater likelihood of engaging my state and local politicians than I do my federal representatives, and while New Hampshire residents have more direct representation than, say, California residents, it's still dramatically improved over our representation by federal reps.
This of course comes with its own set of pitfalls, for which the federal government has been placed as arbiter, and ceding / being granted power with which to remedy, but in my opinion, term limits seem to be more of a band-aid for a hemorrhaging wound than a a root cause fix.
I felt the author made a good point related to this, that the current system, and the current belief in its self-corrections, may be a serious problem during deadlock:
"When politicians today praise America’s system of checks and balances, they seem to understand it as a self-correcting mechanism: When one branch pushes too hard, the other branches must push back, preserving equilibrium. That understanding actually encourages politicians to overreact, in the belief that they are playing a vital constitutional role. It also encourages complacency, because a system that rights itself requires no painful compromises to preserve."
The problem the author points out with the American constitution is not that we have deadlock, and then we must compromise to get around that deadlock. The problem the author points out is that we can get deadlock, and the system itself has no recovery mechanism for bad actors; deadlock makes it possible for the entire system to collapse. Parliamentary systems have new elections when the existing government cannot reach a deal. That is, the system itself has a failsafe for true deadlock.
"Deadlock is good" works in a system where the disagreeing sides are reasonable and willing to debate and compromise to produce a solution with broader support.
That is not the system we have: we have a fully-polarized system in which each major party's agenda consists primarily of ensuring that the maximum number of items from the other party's agenda to be enacted will be zero (I say "maximum", because rolling back or repealing any previously-enacted items is also an option). Since they're both quite good at the tactics, the result is inaction even in times when action is needed, to the detriment of the American people.
> "Deadlock is good" works in a system where the disagreeing sides are reasonable and willing to debate and compromise to produce a solution with broader support.
This is not correct. Sometimes inaction is much better than action. In the case of a corrupt government, inaction is always preferable.
The US constitution is built to create deadlock. See checks/balances. It is this deadlock that has lead to American prosperity. While it is unable to do good, it is also unable to do harm.
The constitution was built to create compromises and shared power. It was not built to create deadlock.
The question this essay asks is, how effective is it at those goals? Are there situations where it could all collapse? If yes, are there other systems which are less likely to collapse?
I suppose if you believe that the only correct amount of government action is zero, you might feel that way. But some of the rest of us enjoy having things like property rights.
Actually, deadlock should be the normal state of affairs. The world doesn't change that much from year to year that the federal legislature has to do a whole lot.
People who complain about "deadlock" are really complaining Congress isn't implementing their legal and budgetary priorities. But that isn't because there's something wrong; that's because not enough of their countrymen agree.
The idea that any action is needed at all is often incorrect. Sometimes the best thing to do is nothing.
A perfect case in point, the patriot act and the department of homeland security. That represented action taken. Solutions developed. Where they the right actions and the right solutions? Not in the least. Would we be better off without them? Probably.
Indeed, and you hear these kinds of suggestions all the time.
It sums up the absurdity of the situation when it's genuinely and routinely proposed that a solution to ridiculous cost of living in a city is to live.. not in the city.
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.