This is a good general tool for less-mathematically-deep folks to keep in their pocket: look for well-behaved objects that do something nice under the operation you're interested in. Typical "well-behaved" objects do things like stay where they are, or end up as a constant multiple of themselves, or end up as 0 or 1, or something like that. Then try to represent everything else in terms of those objects, so that you can take advantage of their convenient behavior. Less-difficult examples include:

- Prime factorization: primes have nice properties, and you can turn every integer into a product of primes (polynomial factorization is an extension of this idea) and work with the nice prime properties

- Vector spaces: basis vectors have nice properties, so you write vectors as sums of them and do operations on the coefficients instead of the vectors themselves

- The exponential function: it's the unique function with f'(x) = f(x), so you try to turn everything else into exponentials anytime you have to solve some painful differential equation because you know those terms will go away

- Fixed points in dynamical systems: if you don't want to analyze how arbitrary things change, find the points that don't, then think of the other points as (fixed point) + (small perturbation) and reduce your work to handling the perturbation

- Taylor series: polynomials are easy, smooth functions are hard, so turn your smooth function into a polynomial and do polynomial things with it

I've been meaning to publish the tips that we send to people who email us asking for Show HN advice. Anybody want to add anything? or see anything incorrect?

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Read https://news.ycombinator.com/showhn.html. Point users to something they can try out for themselves. Don't require signups or permissions that aren't obviously needed. Avoid popups. Avoid overly slick website design and (especially) marketing language: HN users tune all that out and in fact it hurts you. Text and text-based layouts are good. Information density is good. Avoid super-large fonts and excessive pictures, they make you look lightweight. Put intellectually interesting details up front. If you're launching a company, corporate branding is fine; otherwise it's a negative, so tune it down.

Add a first comment to the thread with the backstory of how you came to work on this and explaining what's different about it. This tends to seed better discussion.

Make it easy to tell what the product/project is; otherwise the discussion will consist of "I can't tell what this is". Link to any relevant past threads.

Your primary mission is to engage intellectual curiosity. If you try to sell HN readers on your stuff, you'll evoke objections. Engage their curiosity and they will sell themselves.

Mention areas you'd like feedback about or open questions. Surprising or whimsical things that came up during the work are also good--they are unpredictable and that makes them interesting.

A little humor is ok; more than a little feels presumptuous. Don't be chummy, just answer straightforwardly. Don't address other users by their usernames (it's not the convention on HN and feels out of place). Don't introduce yourself more than once.

Don't say nice things about yourself or your work. It invites comeuppance. Instead, be humble or even mildly self-critical; then readers will look for nice things to say, and even when finding fault, won't make as big a deal about it.

Don't ask for upvotes. Our software ignores most promo-votes, plus HN users notice them and get mad. Especially make sure that your friends don't post booster comments or softball questions. HN users sniff that out a mile away and then we have to kill the thread.

Email us a link to your submission when it's up and we might be able to give you some help or make sure it doesn't get flagged.

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This originated as advice for YC startups but I always liked the pg/yc tradition of giving the same advice to everybody.

> you will need to spend 10x effort than an ordinary Chinese kid

I really don't think this is the case. An ordinary Chinese kid is learning Chinese 24x7 -- for decades. If you start learning a new language when you are an adult, the expectation seems to be that you'll be both fluent and proficient in a few years. There is a myth that children are able to do this.

It's just not true. Talk to a 5 year old. They have mediocre fluency, and very little proficiency. The average English speaking 5 year old only has a vocabulary of 5000 word families. Contrast that to the average high school student with over 15,000 and the average university graduate of over 20,000. Even by 10 years old, try plonking them down in front of the news and ask them to summarise what was said. Most 10 year olds can't do it, because they lack both vocabulary and grammar. Look at English text books for junior high school students. Note how basic the English is. And still many students struggle to comprehend (though by the time a child is 10, they have pretty amazing fluency because that's what they practice all day, every day).

I guarantee that you can vastly outperform a child in learning a second language if you spend comparable amounts of time and effort. I say this having taught English as a second language.

Now you may ask why, after years of study and frustration in classes that most students can produce no language. The main reason: if you don't review every day, you will hit a ceiling pretty fast. Students usually have class 1-3 times a week for 1-2 hours per class. This is literally useless. 5 minutes a day, every day, will give you dramatically better results.

The next biggest reason: teaching fluency is unpopular because historically many teachers never achieved any real fluency (and they inflict the poor teaching they received on the next generation). Also, fluency is virtually impossible to test objectively and takes a huge amount of teacher time to even evaluate. I worked it out one day. I was expected to work in classes where my opportunity for 2 way conversation in the class worked out to less than 30 seconds per student per hour. Pretty much guaranteed failure.

Next biggest reason: Students are told that 2000 words of vocabulary will make them fluent, and so limit themselves to this level (that is surpassed by 3 year old native speakers -- talk to a 3 year old and judge for yourself). Students also forget the frustration of being a child and not understanding what's going on. Children frequently burst out in tears and tantrum all over the place because they are so frustrated. We have this idea that the acquisition of our first language was effortless, and so wonder why we need to spend so much effort in the next language. Next time you talk to a child, question why they don't understand what you are saying. Very often the surprising answer is because they don't speak English very well!

And finally (finally for this already long email, not because I ran out of reasons): Adult speakers are unwilling to act like children. They are unwilling to put themselves in situations where they do not understand what's going on and where they have no control over their surroundings. They are unwilling to be silly, and to make mistakes and to interact with language resources that are aimed at their level (like cartoons). Again, watch a 4 year old. Copy them. (The same Spongebob episode 500 times in a row until you are repeating the lines to yourself as it is playing). It's not because it is harder as an adult. Just the opposite. As adults we are so used to having thing be so easy that we are reluctant to put in the effort of a 4 year old.

Yes, at FedEx, we considered that problem for about three seconds before we noticed that we also needed:

(1) A suitable, existing airport at the hub location.

(2) Good weather at the hub location, e.g., relatively little snow, fog, or rain.

(3) Access to good ramp space, that is, where to park and service the airplanes and sort the packages.

(4) Good labor supply, e.g., for the sort center.

(5) Relatively low cost of living to keep down prices.

(6) Friendly regulatory environment.

(7) Candidate airport not too busy, e.g., don't want arriving planes to have to circle a long time before being able to land.

(8) Airport with relatively little in cross winds and with more than one runway to pick from in case of winds.

(9) Runway altitude not too high, e.g., not high enough to restrict maximum total gross take off weight, e.g., rule out Denver.

(10) No tall obstacles, e.g., mountains, near the ends of the runways.

(11) Good supplies of jet fuel.

(12) Good access to roads for 18 wheel trucks for exchange of packages between trucks and planes, e.g., so that some parts could be trucked to the hub and stored there and shipped directly via the planes to customers that place orders, say, as late as 11 PM for delivery before 10 AM.

So, there were about three candidate locations, Memphis and, as I recall, Cincinnati and Kansas City.

The Memphis airport had some old WWII hangers next to the runway that FedEx could use for the sort center, aircraft maintenance, and HQ office space. Deal done -- it was Memphis.

That's how the decision was really made.

Uh, I was there at the time, wrote the first software for scheduling the fleet, had my office next to that of founder, COB, CEO F. Smith.

"This is a Golden Sunrise carrot, in burnt orange with off-green foliage. Heritage. What do you think?"

"Very nice, Bateman," Bryce replies. "When did a dork like you get so tasteful?"

It's all going well, and then Van Patten places his carrot on the table. It's fucking magnificent.

"This," he says, "Is a Pioneer Ridge carrot, in deep ochre with leaves in a color called 'hazy forest.' The seed stock is heritage, and the planting was organic."

"Amazing," says Bryce. "This is the best carrot I've seen all day."

I can't believe Bryce prefers Van Patten's carrot to mine.