I think swombat was definitely rude in his first comment calling it a "fart" and "trash". Name-calling is labeling, and is neither accurate nor helpful in a cognitive sense; and is abusive and disrespectful in a social sense; and it appears to be based on a strong personal emotion of anger, rather than an objective appraisal. It has no place in a civil and intellectual forum. But this is the internet. It's never been a civil and intellectual forum, including here, despite what many HN users would like. Even associate professors, when online, do it: http://news.ycombinator.com/item?id=1611007

The best we can do is to seek the grain of truth in what someone says, because they often do have a point, disregard the rest, and not fall into name-calling ourselves. It's just about impossible to stop someone from being rude; but we can stop ourselves from taking it personally. And the most effective way to do that is to fully accept any legitimate criticism they have, and totally discard the rest. The rudeness belongs to them, not to you, and you can bet it causes them all sorts of problem. One should therefore feel sympathy for person who has been rude (including oneself.)

That said, let me unpack what (I think) was meant: by "brain fart", he's upset about the writing itself, and that the ideas have not been thought out carefully. He sees it as carelessness, and is offended. Whereas I see it as a lack of ability, with English not being the authors' first language. But I agree that you and the other authors can improve on this - as he said "you can do better than this".

By "link-bait trash", I think he means that you have written this article for the purpose of getting hits, and not primarily out of interest in the content, nor for a wish to communicate it. From the article, and what you've said here, it does come across that way - but I find it very hard to judge, because of the language issue. Poor communication can lead to all sorts of problems!

He could have written these thoughts out objectively, without name-calling; as a result of not doing that, he has offended you. When a person feels attacked and offended, it is distracting for them, and makes it difficult for them to appreciate the actual content of the criticism (it even tends to pressure people to go against the criticism). Name-calling undermines one's purpose.

I hope the above makes it easier for you to accept the content, and disregard the insult.

You can begin by asking yourself what the purposes of the article were - was getting hits the primary purpose? It might not be "entirely true", but is it partly true? If so, admit it to yourself, and then you can move on. Having an objective and factual perspective makes you (largely) immune to insult.

(BTW: I have a more nuanced view of writing out algorithms. It's definitely useful at times, but it's not always the best one (not crucial or essential). A danger is that writing can concretize your conception of the problem (eg an incorrect assumption); whereas beginning to code can give you information. Have you ever gone to a lot of trouble to get clear on a problem, and then when you start to code it, you immediately realize that you misunderstood it, meaning that all that time was wasted? (and if you've become attached to that misunderstanding, you may fight the evidence, or not even see it, because not open to it). Writing algorithms definitely has its place, it's a mix.)