Or you can hand wave a bit and trust intuition. Just like the titans who invented it all did!
The obsession with rigor that later developed -- while necessary -- is really an "advanced topic" that shouldn't displace learning the intuition and big picture concepts. I think math up through high school should concentrate on the latter, while still being honest about the hand-waving when it happens.
I broadly agree. But, the big risk here is that it's really easy for an adventurous student to stretch that handwaving beyond where it's actually valid. You at least have to warn them that the "intuitions" you give them are not general methods, just explanations for why the algorithms you teach them do something worthwhile (and for the ones inclined to explore, give them some fun edge cases to think about).
You can do it with synthetic differential geometry, but that introduces some fiddliness in the underlying logic in order to cope with the fact that eps^2 really "equals" zero for small enough eps, and yet eps is not equal to zero.
calculus works... because it was almost designed for Mechanics. If the machine it's getting input, you have output. When it finished getting input, all the output you get yields some value, yes, but limits are best understood not for the result, but for the process (what the functions do).
You are not sending 0 coins to a machine, do you? You sent X to 0 coins to a machine. The machine will work from 2 to 0, but 0 itself is not included because is not a part of a changing process, it's the end.
Limits are for ranges of quantities over something.
Fair question. Outside of a few prototypes and experiments, we don’t really use Rust in production (yet).
The company as a whole uses a pretty wide range of languages, but for this project the baseline was Java/Quarkus. The discussion wasn’t “are we allowed to use Rust?”, but whether bringing it in for this new component made sense given team ownership, ops, and how early the project still was.
Besides being a bit of a shallow comment, what exactly do you imply here? That capitalism logically implies that the rich become richer? I don't think this is necessarily the case, it just needs a stronger government than what the US currently has in place. (e.g. progressive taxation and strong antitrust policy seem to work fairly well in Europe).
But with how compounding works, isn't this outcome inevitable in capitalism? If the strong government prevents it then the first step for the rich is to weaken or co-opt the government, and exactly this has been happening.
>That capitalism logically implies that the rich become richer? I don't think this is necessarily the case,
It doesn't need to imply anything. It's an ideology, those promoting it will say whatever BS attracts people to it. In practice, what is happening in capitalist countries since 1970s (when they abandoned all pretense) is that the rich get way richer and everybody else is fucked.
At the end of the day Capitalism and Communism have nothing to do with authoritarianism and liberalism/democracy. An authoritarian capitalist country is a perfectly valid type of government as there has never existed a 'pure' capitalistic governed country.
Proven outcomes in the real world matter, not hypotheticals in a textbook. Can you provide clear examples of successful communist nations where you would be willing to live and raise children, or is this just pseudo-intellectualism?
All communist nations have implemented the same exact narrow subset of the ideology that we know as Marxism-Leninism.
The reason being that everyone else who tried something more e.g. democratic generally got crushed. So the commies that ended up running countries in the real world were the most ruthless, hyper-violent ones.
Right. To me the conclusion is that communist theory is fatally flawed. Real world application shows that every real, practical communist system will rely on hyper-violence and ruthlessness to preserve itself. Therefore the average person is better off in a capitalist system than a communist one. Can you refute this conclusion?
> That capitalism logically implies that the rich become richer? I don't think this is necessarily the case,
It is necessarily the case. Capitalism is characterized by private ownership of capital, which among other things means that it's possible to accrue it without limit. So the loop whereby the rich accumulate capital, which then allows them to extract even more value produced by workers (i.e. people who actually do useful things with said capital), is an inherent part of capitalism.
You can make it more mellow by heavily taxing the capitalists and using that money to raise the standard of living for everyone else, which is basically what Western social democracy is. But it doesn't eliminate the loop, and thus rich continue getting richer. And more powerful, too, which they use to dial said taxation back eventually.
We have a lot of people, capitalism values them as approaching zero, anything that alters that valuation (without reducing population) is contrary to capitalism. Capitalism means the rich must get richer, they own the resources and means of production, they take the reward.
It comes to a point where they need an underclass to insulate them from the masses; look how cheaply Trump bought his paramilitary though, he only had to spend the money taken from those he's suppressing, didn't even have to reduce his own wealth one bit; the military and his new brown shirts will ensure the rich stay rich and that eventually there is massive starvation (possibly water/fuel poverty first).
Or USA recovers the constitution, recognises climate change and start to do something about it.
It seems like the whole of humanities future hinges on a handful of billionaires megalomania and that riding on the coattails of Trump's need to not face justice for his crimes.
Capitalism just means private citizens can own the means of
production (e.g. start a business, buy stock) and earn a return on investment. It doesn’t mean only the rich must get richer. It means anyone who saves and invests their money instead of spending it gets richer.
However capitalism is perfectly compatible with a progressives taxation system such that the rich get richer at a lesser rate than the poor get richer.
>anyone who saves and invests their money instead of spending it gets richer.
You realise that a large swathe of society earn less than their costs?
Everyone will get richer perpetually, there will never be any impact on climate, we'll never suffer water shortages, we'll all ride unicorns and eat rainbows...
The important thing to note here is people have been propagandized into thinking that capitalist = democratic. In fact the US would gladly punish you with 'un-American activities' investigation if you said anything to the contrary.
The thing is a capitalistic country will gladly turn itself into an authoritarian one if both wealth becomes concentrated and wealth buys votes. With the massive rise in authoritarian activities all over the world, especially in the US our democratic system is at very high risk of collapsing.
I did a BK search earlier in the article and ended on the same page, decided I couldn't be bothered to play those sort of games and clicked away. The GPs link actually looks rather interesting so I'll investigate, so take this a hate-it-folk vote.
Understandable; let me ask a a question. You don't want to play these sort of games (read a paragraph, enter a word). For you, browsing to find a compelling devtool, what makes you say, this is legit? Can you share examples of a couple of sites that do exactly what you are after?
I say that not because we wanted the CLI homepage to be 'legit', the light context there is we needed a way to quickly change direction from a previous failed initiative that added stark category marketing across the classic site... so took the opportunity to do purposefully do something very different from conventions, rightly or wrongly.
I'd never heard of BK before and I see some positive opinions on HN; I manage a small company's CI, we're really rather happy with GitLab CI, but I'm always on the lookout for something better. Clicking through to your page I'm looking to quickly find out what are the features, why it's different, how much it costs ... and for that a boring, routine website is what I'm hoping for. I'm very much not against the command-line (most places I work people complain that I use the command line when "there's this really good GUI"), but command-lines are hard, they need to be learned -- when I'm just looking for the outline as to whether it's worth digging further I really don't want to have to learn your command-line in order to get it, boring and routine is better. Just one grunt's personal opinion -- best of luck with the business!
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