Mathematics all-in-one cheat-sheet (2013) [pdf] - <AUTHOR> https://ourway.keybase.pub/mathematics_cheat_sheet.pdf <comment><USER2> I think the author's page (Alex Spartalis) deserves to be mentioned:

[https://www.alexspartalis.com/cheat- sheet.html](https://www.alexspartalis.com/cheat-sheet.html)

He has the same version (v2.10) there and mentions that, "The Web version does not include the distribution functions due to file size restrictions. Email me if you would like a copy of these." That explains why pages 213-330 are missing. Someone should offer to upload the full copy to keybase.pub (or someplace) since his personal site can't handle the load.

People sometimes do tremendous work creating a program/book/artwork, and _want_ the world to see it, but don't get around to really share it or promote it.

<comment><USER3> I sent a message using the contact form. Thanks for mentioning this.

<comment><USER4> Just use torrent! It's easy, and potentially free!

<comment><USER3> Distributing new versions is an issue though, as there is no way to tell anyone who is currently seeding the old torrent. But it's not a terrible idea if it turns out there is really a lot of bandwidth (I don't expect that), then I could use my server for seeding at least.

<comment><USER5> Hmm, that sounds like an interesting problem in itself, a torrent client that handles versioning and updates behind the scenes.

<comment><USER6> I mean, thats essentially the apple app store right? Just with torrents and documents instead of apps? So like a freely distributed google docs, but for everything. That movie you downloaded a week ago got a better version, the sci-hub article you downloaded last week has commentary from the author or has been disputed, That microsoft office (excel, word, onenote) you've been working on with a group has a long revision history and automatic version control. You could even download the 'latest version' at 'run-time'; when you double click to open the document. There's a company, or atleast the very start of one in these ideas.

</comment></comment></comment></comment></comment></comment><comment><USER7> Wow, I have to say I feel somewhat bad for the author who spent so much time (months?) compiling this semi-comprehensive reference work. There's so much information, but at the same time, so little useful information to any particular reader. It's so broad as to be a hindrance to using it in any sort of daily reference.

Who would use this? Wouldn't you probably resort to a reference more specific to your field?

Is this the product of someone's superficial fascination with mathematical equations combined with OCD to copy down everything ever read, gone awry? Or is this like a strange version of a Noah Webster?

<comment><USER8> Well, I find it extremely useful.

This is my new go-to item when someone asks me, "What would you bring with you if you could go back in time to the year 1600?"

<comment><USER9> I thought I was the only one who pondered that! I think we'd have even more fun times in 1st century CE Alexandria.

<comment><USER5> They'd burn you at the stake.

</comment></comment></comment></comment><comment><USER10> Cheat-sheet we were allowed to use during math exams at university:

Theoretical Computer Science Cheat Sheet [https://www.tug.org/texshowcase/cheat.pdf](https://www.tug.org/texshowcase/cheat.pdf)

It's 10 pages, so 3 papers with one page free for something that might be missing.

<comment><USER11> I often used this when solving assignments and can recommend it to any computer science student.

</comment></comment><comment><USER12> Making your own cheat sheet is half the battle when you are trying to learn the topic. I remember in my 4th year Stochastic Processes class [0] (back in 2005, wow) we could bring in a double sided page of notes. I wrote my sheet up in LaTeX [1] and shared it with the class, of course this made it better by having others contribute. Some didn't understand why I would "help others out" by giving it away, but I never understood that, like a page of formulae are going to get you an A (also why not help others out?).

Of course after spending so much time developing the formula sheet and working through the example problems (always the most important thing you can do), I think I looked at the sheet twice in 3 hours during the exam.

Also, Dr. Glen Takahara, this class and your instruction are one of my fondest memories at Queen's!

[0] [http://kje.ca/school/stat455/cheat2.pdf](http://kje.ca/school/stat455/cheat2.pdf)

[1] [https://mast.queensu.ca/~stat455/](https://mast.queensu.ca/~stat455/)

</comment><comment><USER13> Nice touch: 4.15 FERMAT'S LAST THEOREM: ... General case when n>2 was proved by Andrew Wiles (1994). The proof is too long to be written here. See: [http://www.cs.berkeley.edu/~anindya/fermat.pdf](http://www.cs.berkeley.edu/~anindya/fermat.pdf)

<comment><USER14> I actually can't tell if that was an intentional "margin" joke, or if the author is just bluntly stating a fact about Wiles' proof...

EDIT: Nope, probably intentional. The author doesn't say something similar for any other proof based on a quick CTRL+F :)

<comment><USER15> Fermat wrote that in the margin of his book Arithmetica that a proof existed, but there wasn't space in the margin to write it. It took Wiles 385 years to find a proof, and it won't fit in a margin. [https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem](https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem)

That's the allure of the theorem; that a simple unknown proof may exist.

<comment><USER16> Yes, I remember when news of his proof broke, being disappointed at how voluminous and obscure (to someone like me) it was. I'd been hoping for something I might be able to get my head around. (Hard as it was, I don't think Wiles spent 385 years coming up with it btw!)

<comment><USER17> Whether there is an existing and verified proof or not, there is still a great mystery to be solved by figuring out what Fermat actually meant by what he thought as an elegant solution, whether it is an actual solution or not.

<comment><USER18> Well, it could have been like Kempe's chains... they finally realized there is a problem, and then it took like 100 years before Appel and Haken made what is probably the first computer-aided proof. And who can say it's really a "proof" if it doesn't explain "why" it's true.

</comment></comment></comment></comment></comment></comment><comment><USER19> I like the idea of this, but I'm not sure that "cheat sheet" is the best term for it, given that it weighs in at quite a few pages (191 physical).

<comment><USER20> The sort of ~100 page softcover reference book that we were permitted to use in highschool math, physics, and chemistry exams is called around here, literally translated, a book of tables. The term is probably a remnant from a time before pocket calculators when it contained actual trig and log tables. "Book of formulas" would probably be a more apt name nowadays. Not sure if there's a common word for such a thing in English.

<comment><USER21> This kind of thing? [https://en.wikipedia.org/wiki/Abramowitz_and_Stegun](https://en.wikipedia.org/wiki/Abramowitz_and_Stegun)

I'm not sure there's really an English word for it. That's strange.

<comment><USER22> Normally, I've heard others reference books like A&S as a "handbook."

It's even in the formal title.

<comment><USER21> Right. Only "handbook" is so broad. It could be about any subject.

</comment></comment></comment></comment></comment><comment><USER23> I got a B in probability because I didn't write a proof of the central limit theorem on the allowed cheat sheet for the final exam. So of course it's the first thing I looked for on this one. It's not there.

<comment><USER3> A B is like 80% or so, judging from A being the best iirc? I'm not familiar with alphanumeric grading systems.

<comment><USER24> Things can get a bit customized at either end of the spectrum, but generally each letter covers 15%, with A..D covering the span 100% to 40%.

So a B would be 70 to 85.

<comment><USER25> Shouldn't that sort of grading be on a bell curve? That would seem to be the fairest.

<comment><USER26> Many smaller (<60 students) math classes, in my experience, have bimodal distributions of scores, so a bell curve by definition simply doesn't make sense. In addition, there's been a move to standards-based or mastery-based grading, that is, grading according to what you know of the material rather than how you compare to your neighbor. This allows comparisons over time and consistency with regard to subsequent classes -- if you have a C as a prerequisite for the next class, then a C should indicate the same mastery of material rather than the same relative position in the class.

</comment></comment></comment></comment></comment><comment><USER27> More "Cheat Book" than "Cheat Sheet" :)

Looks like it could do with typesetting in LaTeX - I think the author started doing this here: [http://mathscheats.weebly.com/](http://mathscheats.weebly.com/) but never entirely completed it. Plenty there to chew on though.

</comment><comment><USER28> Ah, 10% of the first section of the CRC Handbook of Chemistry and Physics, with amateur typography. Sort of like Greenspun's tenth rule, but for math.

<comment><USER29> I've heard of mathematicians handwriting proofs in the margins of books. Like an MVC, I can appreciate the data without appreciating the presentation.

</comment></comment><comment><USER30> While we're on the topic of this kind of thing: [https://en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics](https://en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics)

<comment><USER31> This is an excellent book, but perhaps a bit dated despite the fact that Mathematical Books have a long shelf-life. Factoid: The book is noteworthy because it was a major source of information for the legendary and self-taught mathematician Srinivasa Ramanujan who managed to obtain a library loaned copy from a friend in 1903...

</comment></comment><comment><USER32> It's awesome. Though I prefer my Bronshtein :D [https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev](https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev)

<comment><USER33> Interesting - I've had the German version from my university days (every ME student had one) and it's spelled "Bronstein". The English spelling makes me a little dizzy.

</comment></comment><comment><USER34> When I was studying mathematical physics, my classmates and I made similar quick reference notes in latex. Based on a cursory look, it seems to be missing some important complex analysis and abstract algebra/lie theory results (although I haven't read what the author studied).

<comment><USER35> Searching for stuff I've used, this document is also quite light on combinatorics, complexity theory, and order theory (and of stuff I haven't used much, I don't see anything on category theory or topology). I don't think 330 pages is nearly enough to be truly all-in-one.

<comment><USER14> Agreed. This document is reasonably broad but it's missing quite a lot of undergrad mathematics, let alone graduate math.

If you literally wrote down sequences of definition, theorem, proof, definition, theorem, proof, ... with no exposition or exercises whatsoever, I think you might be able to include most undergraduate math in about 1000 pages. That would include calculus, real analysis, complex analysis, linear algebra, abstract algebra, discrete math. Maybe elementary number theory, topology and probability theory as well. That would be...horrible to learn from, frankly. Imagine a ten volume set of Baby Rudins, with no exercises.

If you really doubled down on the cheat sheet angle and didn't include any proofs - just the theorems, identities and inequalities - I think you could get through all undergrad math in a few hundred pages. But you wouldn't have any of the peripheral content the author included, like physics/economics.

<comment><USER34> 'Riley, Hobson and Bence' was a standard reference I used throughout my undergrad and graduate studies. Sure enough, it's about 1200 pages.

</comment></comment></comment></comment><comment><USER36> You know you're in for a head banging when the Table of Contents is 25 pages long! :o

<comment><USER37> [https://archive.org/details/elementsquaterni00hamirich/page/...](https://archive.org/details/elementsquaterni00hamirich/page/n13) Hamilton's "Elements of Quaternions"'s table of contents is about 60 pages long and includes footnotes.

</comment></comment><comment><USER38> It is interesting and fun! I have a loose suggestion - it could be published together with LaTeX codes for any formula present - so it would be great speed up for someone who wants to use various formula in his works. However the choice of various areas is strange for me ( partially lack of some engineering areas, partially lack of very basic physics things, partially lack of mathematics) A lot of things is missing: Maxwell-Clerk equations. Einstein equations. Schrödinger equation. Dirac equations. Notable: Laplace equation and Maxwell-Clerk equations, wave equation!!! Harmonic oscillator equation. Quantum physics, Heisenberg relation at least please! Hydrodynamic, notable no Navier-Stokes equations. Special functions: Bessel, Jacobi, Lagrange, Chevyshev polynomials, various equations related to it. No elliptic functions, no Weierstrass function mentioned. No various number theory objects: Mobius function, Minkowski function ?() not mentioned. Congruences nearly omitted ( Chinese remainder theorem maybe) Group theory, some simple results from category theory, Shannon theory completely missing. No universal algebra. No basic cryptography. Complete lack of various numbering systems ( binary, hex at least)

</comment><comment><USER39> Find a bug in page 39: y' is Lagrange's notation while dx/dy is Leibniz's.

</comment><comment><USER40> Seems very similar to a classic formula collection like [https://dlmf.nist.gov/](https://dlmf.nist.gov/)

</comment><comment><USER41> _One day_ , I'll make an Anki version of this.

<comment><USER42> Speaking of, can anyone commend some good Anki mathematics decks?

<comment><USER43> There is just one link here: [https://learnawesome.org/learn- awesome/mathematics.html](https://learnawesome.org/learn- awesome/mathematics.html)

If people share links here, I'll send a PR to learnawesome to add those under mathematics#flashcards section.

</comment></comment></comment><comment><USER44> First time I've seen someone use Keybase.pub. Last time I checked they gave out 250gb for free for everyone... this is a good use of that!

<comment><USER45> I wonder how long that can last before abuse kills the system. Some quotes from their page about KBFS [0]:

"The 250GB free accounts will stay free"

"we'll never run an ad-supported business"

"we're not trying to make money"

[0] [https://keybase.io/docs/kbfs](https://keybase.io/docs/kbfs)

<comment><USER46> How _is_ Keybase funded anyway? They say they're hiring, so money is coming from somewhere.

<comment><USER47> Their Series A raised $10.8M back in 2015: [https://keybase.io/blog/2015-07-15/keybase-raises- series-a](https://keybase.io/blog/2015-07-15/keybase-raises-series-a)

</comment></comment></comment></comment><comment><USER48> I remember using something similar called "Mathematics Handbook for Science and Engineering" in university. [https://www.amazon.co.uk/Mathematics- Handbook-Science-Engine...](https://www.amazon.co.uk/Mathematics-Handbook- Science-Engineering-Lennart/dp/3540211411)

I assume there are many others, and this is a free alternative.

</comment><comment><USER49> nice work. I would have removed

most of 'PART 1: PHYSICAL CONSTANTS', 'PART 8: APPLIED FIELDS', 'PART 18: ELECTRICAL', and some of 'PART 99: CONVERSIONS'.

"all-in-one" math seems enough :). Other stuff seems arbitrary and leaning towards physics (which could have its own giant book).

<comment><USER50> I'm biased as I'm an EE, but I'd say that the Laplace transforms within the Electrical section are firmly in the realm mathematics, so keep them. It just so happens that they are only really useful in the domain of digital signal/control processing, and I think to get the true form or radioactive decay(?) though I may be mistaken. I'd put it next to information on Fourier transforms. The circuit theory may be a bit unnecessary though I agree.

</comment></comment><comment><USER51> It's a very fine compendium of notable relations.

At 212 pages long, it's certainly not a cheat-sheet.

If it didn't have obvious spelling errors I might be more confident the rest has been transcribed accurately.

</comment><comment> r-w Things get kind of pixelated for me around page 123. Anyone else?

<comment><USER52> You are not alone. Seems like formula's are not vector anymore from page 121.

</comment></comment><comment><USER53> Add this to the list of items (or perhaps the only item?) you'd take if you'd time travel to the past

</comment><comment><USER54> I've owned paper copies of Murray Spiegel's Schaum Outline of Mathematics, and even the government-funded Abramowitz-Stegun doorstop, this reminds me of those somewhat, but the title is misleading as it has as much physics and chemistry as mathematics.

</comment><comment><USER55> Pages 168 to 262 seem to be missing?

<comment><USER56> Fermat's Lost Theorem?

</comment></comment><comment><USER57> I hate how often these sprawly things are called cheetsheets:

      LOGIC SYMBOLS
      Symbol Symbol Name Meaning / definition Example
        &        and     x & y

</comment><comment><USER58> Slightly off-topic: from a security perspective, how safe/not safe is it to be clicking open random pdf's? Wouldn't this be a possible avenue for malware?

<comment><USER59> [https://github.com/osnr/horrifying-pdf- experiments](https://github.com/osnr/horrifying-pdf-experiments)

[https://www.alchemistowl.org/pocorgtfo/](https://www.alchemistowl.org/pocorgtfo/)

Yes. Not only is it possible but historically _already_ an avenue of attack.

</comment></comment><comment><USER60> Awesome! It only serves to remind me I know practically nothing about Mathematics. "Good Primes" and "Happy Primes" .. who'd have thought it ...

</comment><comment><USER61> To me this seems to be exclusively undergraduate mathematics that one might learn in an engineering program. No mention of topology or modern algebra.

</comment><comment><USER62> It's organized like a debate file. Fascinating.

</comment><comment><USER63> Reminds me of the old Schaum's Outlines, I still have a couple of them on the book shelf from college days, saved my bacon many times.

</comment><comment><USER64> Uh, this is a book.

</comment><comment><USER65> OK, so, I also hate to be "that guy", but, despite the admirable effort put into creating this by the author, I am sad to say I don't see why some people are excited about this... Because unfortunately after just looking at a few pages, I saw lots and lots of error and misleading or plain confusing statements, basically on every single page I looked at closer, which makes me distrust it. Granted, these vary in their severity, but still...

Examples:

\- p. 50, definition of a complex vector space, says " A complex vector space consists of the same set of axioms as the real case, but elements within the vector space are complex.". The vector space does not "consist" of the axiom, it adheres to them. And it makes no sense to say that the "elements" (vectors) are "complex". Rather, that scalars are allowed to be complex, not just real.

\- p. 50: definition of a subspace is a mess. To pick just one obvious problem with it: What even are "axioms (a) and (b)"? Perhaps the three unlabeled "axioms" at the top of the page are meant (being closed under addition, additive inverses, and scalar multiplication)? But certainly the third one (axion "(c)"?) needs to be verified, too (whereas the second, about additive inverses, is redundant).

\- p. 51 the examples at the top of the page end with mentioning C[a,b], the set of all continuous functions on an interval [a,b]. But then it claims that this is actually _not_ an example, because "it has infinite dimensions". But really this is a perfectly fine vector space (also, we haven't even defined what a "dimension" is yet)

\- p. 51, definition of linear independence says "c_1=c_2=c_n=0" which is missing a "=..." before the "=c_n"

\- p. 52 the "general vector" given as a column vector doesn't make sense in a general vector space

\- p. 53: "Matricis"

\- p. 56 "Laprange's theorem" should be "Lagrange's theorem"

\- p. 126: "EXPONETIAL"

\- p. 167: "Matricies", "Prinicples", "opertaions",

\- p. 168: "Determinate"; the formulas for 2x2 and 3x3 matrices implicitly assume a labeling of the entries which is never given, rendering this semi- useless

\- one section is titled "MISELANIOUS"

And on page 38, the fields of real and complex numbers, R and C, are introduced as being written with a "blackboard" font (\mathbb), while on page 51 this is not followed (instead, we get \mathcal{R} and plain C). Why even introduce these conventions if they are then not followed?

Sure, many of these are minor and perhaps even "obvious" mistakes. But if you know the matter well enough to spot all of these, maybe you don't need this cheat sheet? Also, as a mathematician myself, my experience is that the number of spelling mistakes in a research paper (or in anything written and submitted by students) is a good first proxy for the quality of the text: if you can't be bothered to even run a spell checker on your text, should I really trust you to have verified all your computations and logical deductions carefully? (And no, I don't apply this to, say, posts here on HackerNews: I hate it when people shoot down a comment, or a twitter post, or whatever, just because it contains typo. But writing a book is a bit of a different affair, isn't it?).

Hence my point that I wouldn't want to suggest this to anybody as a reference. :-(

<comment><USER66> Page 33: PART 2: MATHEMTAICAL SYMBOLS

</comment></comment><comment><USER67> _misprint_ PART 2: MATHEMTAICAL SYMBOLS

</comment><comment><USER68> I really didn't want to be that guy, and props for the author for such comprehensive reference work, but god, what an _appalling_ typography. Bad tables with too many lines bitmap formulas with misadjusted size, poor spacing, ugly font... Almost everything that could be wrong is wrong.

<comment><USER69> I came here to say the same thing. Looks like the author did not use a good authoring tool to produce good math output.

I generally take notes like this with LaTeX and compile them to PDF but PDFs can be large and if committing to a Git repo can lead to large .git directories. The BasicTeX package for Mac (brew install basictex) has worked well for me: [http://www.tug.org/mactex/morepackages.html](http://www.tug.org/mactex/morepackages.html)

These days I also take math notes as plain HTML files containing Markdown and LaTeX, then render with the TeXme one-liner here: [https://github.com/susam/texme](https://github.com/susam/texme)

I guess what the OP has done here is take all the notes in Word or some other WYSIWYG document editor not specialized for mathematical typography and converted the whole document to PDF. This won't lead to good results. It is absolutely necessary to use tools specialized for mathematical typography to write and publish math.

By the way, is there anyway to create high quality math distributables that are both self-contained and lightweight?

<comment><USER70> Why commit the output files? I generally put "*.pdf" in .gitignore.

<comment><USER71> Probably so that someone can download it without compiling it? GitHub Releases or an equivalent would probably be better, though.

<comment><USER69> That's right. I would like others as well as myself to be easily able to download the PDF files without having to compile it. I tried out GitHub releases and it works okay but not great. I cannot track all the compiled PDFs I have at a single place or move them easily from one system to another like I could with GitHub repos. I am also trying to avoid getting locked into a specific service like GitHub releases.

<comment><USER72> I have very good experiences with Gitlab CI: It just recompiles the PDF(s) from the repository within a minimal docker container (containing a full Tex Live repository) and pushes them online on a website (sFTP or similar). Also Gitlab allows to host the build assets.

</comment></comment></comment></comment></comment></comment><comment><USER73> Not LaTeX; didn't read.

<comment><USER74> I have to admit it's a pretty ugly manual.

Some of those formulas were really blurry, while some of the tables spanned weirdly over pages.

The hosting issues could have been fixed as well if it was LaTeX as it would have been neat in a git repository.

Gitlab also has continuous integration for LaTeX

* [https://www.vipinajayakumar.com/continuous-integration-of-la...](https://www.vipinajayakumar.com/continuous-integration-of-latex-projects-with-gitlab-pages.html)

* [https://sayantangkhan.github.io/latex-gitlab-ci.html](https://sayantangkhan.github.io/latex-gitlab-ci.html)

</comment></comment><comment><USER75> Don't see any logic equivalencies... I think they are kind of neat!

</comment><comment><USER76> Woof. Flashbacks to Sister Mary's Calculus class in 12th grade.

</comment><comment><USER77> Quiet handy and amazing thank you very much for sharing this over.

</comment><comment><USER78> Nice work.

But on page 43 "quadratic" is misspelled.

</comment><comment><USER79> Why does the author not use LaTeX?

</comment><comment><USER80> bet i could fit this on a 3.5in x 5in notecard...

</comment><comment><USER81> s/Cheat-sheet/Cheat-book/g

</comment><comment><USER82> Last page says "Page 212 of 330"

Pages 213+ are probably where they discuss cardinality.

</comment><comment><USER83> Missing the cheats for division (how to rapidly tell if a number is divisible by 3, 7, 2, 5, etc. for prime factorization.)

</comment><comment><USER84> Someday the cover will read e^iτ = 1 and all will be right with the world.

<comment><USER85> Some believe the pi version is superior due to the inclusion of three operators (+, *, exp), and five numbers (0, 1, i, e, pi) which are all fundamental in some sense. The tau version omits the + and the 0.

<comment><USER86> e^iτ + 0 = 1

Fixed.

<comment><USER87> -1 not 1 ...

e^iπ+1=0 from

e^ix=sinx + icosx with x=π

<comment><USER86> Thats why we are using τ not π.</comment></comment></comment></comment></comment>


Ask HN: How much does Y Combinator invest in not-for-profits? - <AUTHOR>

I'm confused about how much amount ycombinator invests in not-for-profit startups?
Is it same $120k or different amount? And i have also heard of $50k donation from teespring?
Can someone clearify me on how much does a not-for-profit gets after joining? What about equity etc? <comment><USER2> YC non-profits get $100k total. YC invests 50k and Teespring matches our donation with an additional $50k.

We don't take equity in the non-profits. The funding comes in the form of a donation.</comment>


DirecTV charges family $400 for equipment destroyed in Colorado fire - <AUTHOR> http://gazette.com/article/1502291 <comment><USER2> Why is this on HN?

I don't understand the problem. Why wouldn't they charge for the lost equipment? That's why you have insurance.

<comment><USER3> "Why wouldn't they charge for the lost equipment?"

Because they care more about happy customers and good PR than a measly $400?

Seriously, the PR hit they're going to take for this far exceeds the value of the equipment.

</comment></comment><comment><USER4> Why doesn't DirecTV insure the equipment against fire? Thus covering the cost of people who've genuinely had a tragic fire, and still able to go after people who should pay?

From the headline I thought it was going to be an automated system still sending letters.

> _Commenting on a complaint from a Mr.Arthur Purdey about a large gas bill, a > spokesman for North West gas said "We agree it was rather high for the time > of year. It's possible Mr.Purdey has been charged for the gas used up during > the explosion that blew his house to pieces." (Bangkok Post)_

</comment><comment><USER5> It doesn't seem like a particularly smart thing to do, since for the sake of $400 they've ensured at least one customer will _never_ use their $10-$50 / month service again...

<comment><USER6> On the other hand, it's a dumb thing to get upset about. Their equipment got destroyed while you were responsible for it, that means you're on the hook for it. If you had insurance, it'll cover it. If you didn't, then you're deeply screwed far beyond the cost of some TV equipment.

Neither side comes off looking at all good here, although DirecTV is definitely in the right, even if not necessarily smart.

<comment><USER3> Being technically/legally in the right and doing the right thing for a customer (particularly one that's suffered a tragedy) aren't always the same thing, not morally (which I doubt DirectTV cares about) and not from the standpoint of customer relations.

<comment><USER6> I agree as far as customer relations, even if it just pissed off this one person it hardly seems worth it. But I think they're both legally and morally in the right here, not that it really matters much.

<comment><USER3> From the update it looks like they already have a policy of forgiving equipment loss in a case of this type. Someone gave the customer bad information.</comment></comment></comment></comment></comment>


A Lecture on Johnson and Boswell by Jorge Luis Borges - <AUTHOR> http://www.nybooks.com/blogs/nyrblog/2013/jul/28/lecture-johnson-and-boswell/ <comment><USER2> It's worth mentioning that Borges is a great author for STEM types. Apart from being a towering critic of literature, he wrote short stories. He treated these as a poetry problem -- compressing the most story into the least number of words. They are spare, lean, but powerful.

 _The Lottery in Babylon_ and _The Library of Babel_ , in particular, are combinatorial horror stories. They take simple concepts and slowly unfold them. The sense of escalating dread at the possibilities of infinity and the _uncertainties_ of infinitude reminds me of HP Lovecraft, yet it's all matter of fact without the purple prose.

I also greatly enjoyed _Tlön, Uqbar, Orbis Tertius_ , where Borges similarly shows the power of mere ideas to reshape the entire world; even ideas which are later shown to be utterly false.

<comment><USER3> Also recommended Borges' "Pierre Menard, Author of the Quixote" about a writer who rewrites Don Quixote word-for-word, though of course imbuing with a radically new meaning given the different historical context:

"It is a revelation to compare Menard's Don Quixote with Cervantes'. The latter, for example, wrote (part one, chapter nine):

'...truth, whose mother is history, rival of time, depository of deeds, witness of the past, exemplar and adviser to the present, and the future's counselor.'

Written in the seventeenth century, written by the 'lay genius' Cervantes, this enumeration is a mere rhetorical praise of history. Menard, on the other hand, writes:

'...truth, whose mother is history, rival of time, depository of deeds, witness of the past, exemplar and adviser to the present, and the future's counselor.'

History, the mother of truth: the idea is astounding. Menard, a contemporary of William James, does not define history as an inquiry into reality but as its origin. Historical truth, for him, is not what has happened; it is what we judge to have happened. The final phrases—exemplar and adviser to the present, and the future's counselor —are brazenly pragmatic.

The contrast in style is also vivid. The archaic style of Menard—quite foreign, after all—suffers from a certain affectation. Not so that of his forerunner, who handles with ease the current Spanish of his time."

<comment><USER4> I was reading this exact passage aloud this very afternoon. It's Borges at his funniest! He's a stand out among the greats, surpassing Joyce, Marquez, Saramago and Solzhenitsyn.

There's a pervasive magic to his writing. The prose equals the subject. It reminds me of the best of Dostoevsky or Bulgakov's trial before Pilate.

<comment><USER5> > It's Borges at his funniest

Exactly. My feeling in the first pages of Fictions was : is it some kind of joke ?

For those who read the House of Leaves, it's good to know that Danielewski took a lot of inspiration from Borges (among other things). If I recall correctly The Garden of Forking Paths is very similar in its purpose and construction.

</comment></comment></comment></comment><comment><USER6> If you are interested in Borges you can't miss the Norton Lectures (1967-1968) that he gave in Harvard. They are available in MP3 format for download: [http://ubu.com/sound/borges.html](http://ubu.com/sound/borges.html) (sadly my original post on HN only had two points and zero comments)

<comment><USER7> Seconded; these have had a permanent place in my iTunes library.

</comment></comment><comment><USER8> Ah, delightful, unread Borges texts still popping up after a four course meal of collected works I got presented with a few years ago (not an English edition). Thanks.

In Lisbon, there's a small, discrete monument to Borges - just a carved stone with a few lines of one of his poems. It is situated in a small garden diagonally opposite the crossroads from the Argentine embassy (GPS 38.736322, -9.142172 ).

I first came across Borges, many moons ago, in an SF collection, with the story of the man who was, recursively, another man's dream ( [http://en.wikipedia.org/wiki/The_Circular_Ruins](http://en.wikipedia.org/wiki/The_Circular_Ruins) ).

But I think he did catch us out with this ([http://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevolen...](http://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevolent_Knowledge)):

        The list divides all animals into one of 14 categories:

        Those that belong to the emperor
        Embalmed ones
        Those that are trained
        Suckling pigs
        Mermaids (or Sirens)
        Fabulous ones
        Stray dogs
        Those that are included in this classification
        Those that tremble as if they were mad
        Innumerable ones
        Those drawn with a very fine camel hair brush
        Et cetera
        Those that have just broken the flower vase
        Those that, at a distance, resemble flies

</comment><comment><USER9> My current bedside reading is: Collected Fictions, by Jorge Luis Borges - [http://www.amazon.com/Collected-Fictions-Jorge-Luis- Borges/d...](http://www.amazon.com/Collected-Fictions-Jorge-Luis- Borges/dp/0140286802) (NOT an affinity link, just the link).

He was a genius. His writing is wonderful. As others have said his ideas are well suited to the kinds of folks who frequent HN. The other interesting thing is that never before have I had people approach me about my reading. But sit in a cafe in San Francisco with Borges and suddenly the world and her friend wants to spark up a conversation about my choice of book.

Cannot recommend this highly enough. If you are looking for reading material that takes you away from technology and work and the usual stuff we fill our heads with, explore the universe through the words of Borges. You won't regret it.

<comment><USER10> When you're done with Fictions, do read the other book, "Selected Non- Fictions" [http://www.amazon.com/Borges-Selected-Non-Fictions-Jorge- Lui...](http://www.amazon.com/Borges-Selected-Non-Fictions-Jorge- Luis/dp/0140290117) (not an affiliate link either)

Not only are they excellent pieces in their own right, you can catch occasional glimpses of the evolution of some of his best stories as well. The biography of Paul Valéry, for instance, foreshadows Pierre Menard.</comment></comment>


Statistical analysis of NFL 4th down strategy - <AUTHOR> http://elsa.berkeley.edu/~dromer/papers/JPE_April06.pdf

<comment><USER2> Could someone provide a TL;DR for this? Frankly, even the conclusion is pretty obtuse.

<comment><AUTHOR> TL;DR for football coaches: If you have a 4th & 2 from your own 10 in the first quarter, go for it!

TL;DR for football fans: The take-away graph is Fig. 4 on pg. 353. The solid line represents when a team SHOULD go for it on 4th down to maximize expected points. The dashed line represents when teams DO go for it. Bottom line is that teams go for it MUCH less often than would maximize their expected points.

TL;DR for economists: NFL coaching could be assumed to be a case where (a) a lot of objective data is available to base decisions on (b) the result to be maximized (wins) would appear to be fairly obvious (c) decision makers (coaches) are highly qualified and highly motivated. Yet in practice, coaches systematically deviate from the strategy that would maximize wins. It's not clear whether this is due to (I) the "true" result coaches are trying to maximize is NOT wins or (II) coaches not making strictly rational decisions.

TL;DR for hackers: I found the analytical reasoning (opportunity cost; etc) interesting, and found it worth reading the whole thing for that.

<comment><USER3> _If you have a 4th & 2 from your own 10 in the first quarter, go for it!_

No matter what the math says, no coach will do this (save for maybe Billichek, but even he's not that bold). Sports is one of those areas where the "gut" and conventions are more important than stats and probabilities. Moneyball is a great book for anybody whose interested in the intersection of sports conventions and math.

[http://www.amazon.com/Moneyball-Art-Winning-Unfair- Game/dp/0...](http://www.amazon.com/Moneyball-Art-Winning-Unfair- Game/dp/0393057658)

<comment><AUTHOR> Actually, there was an article a while ago about a high school coach who NEVER punted or tried a field goal:

[http://sportsillustrated.cnn.com/2009/writers/jon_wertheim/0...](http://sportsillustrated.cnn.com/2009/writers/jon_wertheim/09/17/no.punt/index.html)

I've read Moneyball, and I find it interesting that statistical methods have been accepted so much more in baseball over the last decade or so, but seem to still be shunned in football, at least for this particular situation.

</comment></comment></comment></comment><comment><USER4> Gregg Easterbrook (Tuesday Morning Quarterback column on ESPN.com) has been a huge proponent of "don't punt" and wrote about this paper a couple of years ago: [http://sports.espn.go.com/espn/page2/story?page=easterbrook/...](http://sports.espn.go.com/espn/page2/story?page=easterbrook/060926)

[http://sports.espn.go.com/espn/page2/story?page=easterbrookp...](http://sports.espn.go.com/espn/page2/story?page=easterbrookpreview/070904)</comment>


Show HN: CLI for Email Scraping from Websites - <AUTHOR> https://github.com/lawzava/scrape <comment><USER2> is it possible to add proxycrawl integration with the tool?</comment>


Advice for Graduate Students: Suggestions for a Basic-Research Career - <AUTHOR> http://www.psychology.buffalo.edu/essay.shtml

<comment><USER2> Unfortunately, at this point in time, I feel very strongly that these suggestions will lead you to do good science and end up without an Academic Research position...at least, not initially. Personally, I think we need a revival of Franklin/Jefferson/Priestley/Watt type science, where the science is pursued for fun and interest, instead of for profit. The current petty competition for publications and grant money is the worst thing to happen to science.

<comment><USER3> Maybe we should return university science to the Sputnik Golden Age style of funding: once you've shown that you know what you're talking about, you just get loads of funding and just publish papers to keep it coming. According to folks who were doing science back then, it was glorious; they could get work done so much faster!

And just think of the international consequences. If the US became the land of easy funding, it would definitely keep a lot of foreign talent around. This sort of thing is a competitive advantage, and probably pretty cheap.

<comment><USER4> Seems like the EU is making an effort <http://www.few.vu.nl/~ast/>

</comment></comment></comment><comment><USER5> _4\. If you do basic research, keep your eyes open for applications of your findings._

I'm always reminded of one of my grad school profs who said that the goal of any research should either be commercial or something which will end up in a text-book.

Everything in between is just filler.

<comment><USER6> That is something that really turned me off to academia as I worked through my masters.

<comment><USER7> been there, done that.

</comment></comment></comment><comment><USER8> 1\. Establish an independent niche in the market as early in your startup as possible. Avoid the web2.0 startup trap of following hype implementing ideas that are already popular and profitable. Of course social networks are helpful, but just-another-social-network can't form the basis of your startup

2\. Be problem-oriented, not technology-oriented. Use a variety of technology -- whichever are necessary to solve the problems in the market. As shown by twitter, back in the days of ruby&rails popularity and DIY-everything, it would take twitter considerable resources to assemble a new queueing queuing system which sucks, when existing better alternatives existed. lest the founder be seduced into implementing another overdone component/api in a brand new web2.0/meta-meta-programming language. It is also painful to hear one startup after another say that "we are based on ruby and rails", as if this makes them cooler. While this may interest potential non-technical investors who judge the value of startups by the amount of the lattest technology jargons founders put into their keynote/powerpoints, its simply a waste of resources for the company in the long run. Remember, technology comes and goes, but the underlying need of the market should be the focus of the startup. It is depressing to go to conferences where the same old market problems are tackled; more "cutting edge" techniques, presented by people enamored of the techniques rather than the market problems. If technology is so costly, in terms of equipment, learning time, and other resources, how does one avoid the trap of becoming technique oriented? The answer: use what is already out there, leverage open source and solve real problems in the market.

3\. Think beyond the next hype, or even the next round of investing. Take the long view; look at the big picture. In other words, bite off a piece of question that may take a month, or even a year to answer. There is a major difference between the scientist that wonders how to break the question into appropriate sized grant proposals, and one who wonders how to expand the question into a grant proposal. Furthermore, commit yourself to your question; given the time and energy it takes to answer an appropriate sized research question, pursuing a series of unrelated research questions in parallel rather than in series is often a sign of dilettantism.

4\. If you do developed a new technology in your startup, keep your eyes open for other applications of your findings. On the other hand, if you heavily leverage an existing technology, keep your eyes on underlying technology/framework. Often, the distinction between technology and application is arbitrary and fluid.

5\. When conducting market resource, don't accept data or results at their face value. Keep plugging away at the problem until the answers or results make sense or satisfy you in terms of an overall schema. Most importantly, don't accept other company's solutions (37 signals?); every startup is different.

6\. Expect the unexpected. Many great ideas are discarded because a startup initially "didn't work". However, good execution should provide positive results regardless of the idea involved. Often a "good idea" and a "bad idea" is only differentiated by the execution.

7\. Don't expect quick success in a startup; expect more hardship, sacrifices, sweat, blood and tears. Paul Graham used to tell us that a good startup often require years of work to build up. Perhaps non-entrepreneurs find this aspect of startups strangely frustrating. However, the lack of dedication and handwork differentiate the success and failures

8\. Never stop asking for user feedback. User feedback are the stock-in-trade of startups. The corollary of this suggestion is "never make assumptions." Of course, assumptions are a necessary part of application design, but on an everyday practical level, and in terms of application workflow, assumptions can be disastrous. Many times I've located workflow bugs and inefficiencies in a startup's application workflow, because unlike them, I did not assume that a user could not "go there" or "do that".

9\. Choose a problem that excites you. It should excite you so much that you can't sleep. It should excite you so much that when someone asks you the time, you blurt out your 30 second elevator pitch.

10\. Strive for elegance and cleanliness in yoru code. The elegance of a codebase is in the quality of the thinking and the cleverness of the approach to solving the market's problem, not in the complexity of the design or the sophistication of the technology. Often, the most elegant code are simple, short attacks at the heart of the problem. Study famous open source code in your application domain and appreciate the logic and thought that went into it. All too often startups nowadays ignore existing codebase because it isn't available on github, or dismiss it for using old-fashioned techniques. There is much wisdom and cleverness in some of those old projects. Reading them, learning from them, and citing them, is what real programmers do.

<comment><USER9> Though seems obvious, very good advice esp #1-2</comment></comment>


Cadillac Bets on Virtual Dealerships - <AUTHOR> http://www.wsj.com/articles/cadillac-bets-on-virtual-dealerships-1465172482 <comment><USER2> I'm not so sure about the "virtual reality goggles" idea, but inventoryless dealerships seems like a no-brainer. If I want to buy a Cadillac, I want to test-drive the same model, then pick the options and colours I want, and then have a car to my exact specifications delivered to my door.

The model where I need to scout around to find something vaguely resembling what I'm actually after is ridiculous, especially with something like a Cadillac that can be optioned up the wazoo.</comment>


Ask YC: Should there be an option to hide Karma? - <AUTHOR>

There are many valid arguments to always show karma, but I would suggest that having the choice of customizing your karma display has a net affect of adding value to the site.
The obvious advantage of showing Karma is the feedback it creates to help users learn what is accepted commentary.
On the other hand showing Karma fosters a type of pro Karma group-think, which takes value away from the site.
Anyone have similar thoughts? <comment><USER2> I'm not sure I see the downside of showing Karma. Do you have any specific examples of groupthink in mind?

<comment><USER3> for example, I'd say there is a tendency to upmod an item (without really reading it, or agreeing with it) just because it already has 50 karma.</comment></comment>


Show HN: React Native Demo App - <AUTHOR> https://github.com/Seedstars/reactnative-mobile-app-base <comment><USER2> I can recommend Ignite ( [https://github.com/infinitered/ignite](https://github.com/infinitered/ignite) ) as well, has some scaffolding capabilities.

</comment><comment><USER3> I've been thinking about getting into react native lately, and I needed something like this.

Thank you!

</comment><comment><USER4> I think your README links to the wrong redux.

<comment><AUTHOR> Thanks very much, I copied parts of the readme from another project ([https://github.com/Seedstars/django-react-redux- base](https://github.com/Seedstars/django-react-redux-base)) and those were outdated to</comment></comment>


H3: Uber's Hexagonal Hierarchical Spatial Index (2018) - <AUTHOR> https://eng.uber.com/h3/#hco <comment><USER2> I did some indexing using elasticsearch and some home grown stuff based on geohashes about seven years ago. At the time Elasticsearch was just adding support for geoshape indexing as well. Initially this was also based on geohashes. Later they added proper quad tree support (instead of indexing the geohash as a term), and recently they revamped the implementation using BKD trees. The current implementation is way faster and scalable than what they had a few years back and allegedly quite nice for handling complex GIS data.

What's the advantage of Uber's approach over any of this. Even my primitive geohash solution worked pretty nicely and you can implement it on just about any type of DB. I had a simple algorithm to cover any shape with geohashes of a certain size as well as a quick way to generate a polygon for a circle. The two combined allowed me to do radius searches for any shape overlapping or contained by the circle with simple terms queries on the geohash prefixes. My main headache was keeping the number of terms in a query (i.e. number of geohashes) to a reasonable size (below 1024, which if I recall was a the default limit).

<comment><USER3> They go into some detail on this talk [https://youtu.be/ay2uwtRO3QE?t=712](https://youtu.be/ay2uwtRO3QE?t=712).

What I get from their explanation is that hexagon is a better shape for map grids because they are the most complex shape that can tesselate (the other two are triangles and squares). As they are more close to a circle, distances within a cell are more stable, also computing the distance from a cell center to its neighbours is stable in hexagons as well.

I think the reason hex is not more common is that subdivisions are hard to create compared to triangles or squares. Uber solved this by subdividing in 7 smaller hex and tilting it so they cover the bigger shape with some small overlap.

Also a big problem is distortion, I never thought this would be that huge of a problem but it makes sense. They go into a lot of the details later on the same video.

<comment><USER4> > hexagon is a better shape for map grids because they are the most complex > shape that can tesselate

[Penrose tiling intensifies]

<comment><USER5> I think it's clear what they meant was not actually 'the most complex shape' but the regular polygon with the most sides that can tessellate.

</comment></comment></comment></comment><comment><USER6> I'd be curious to see a more thorough comparison to S2, which IMHO seems simpler (it's just quadtrees) and likely faster (it supports O(1) lookup vs. needing a hierarchical search).

<comment><USER7> The critical advantage of h3 vs. s2 is that all neighbors are equidistant from the central cell. Also, the implementation of the projection means there is less distortion than s2.

I use this library every day and absolutely love it.

<comment><USER8> This is the same reason astronomers like HEALPix tiling for skymaps [0]. Equal areas-per-pixel (important for integrating over areas) with straightforward spherical harmonics calculations and hierarchical extensions that can store images at multiple resolutions by subdividing base cells (LIGO uses one such hierarchical strategy for our low-latency gravitational wave source direction estimates [1]).

[0] [https://healpix.sourceforge.io](https://healpix.sourceforge.io)

[1] [https://arxiv.org/abs/1508.03634](https://arxiv.org/abs/1508.03634)

</comment></comment></comment><comment><USER9> Previously [https://news.ycombinator.com/item?id=16135302](https://news.ycombinator.com/item?id=16135302)

</comment><comment><USER10> Uber really likes hexagons. Their internal name for driver promotions is even "hexcentive"! I've long wondered what compelled Uber to use hexagons to define their various promotion boundaries, because it's not a very user-friendly choice -- the lines on a map look very jagged, for instance.

This post goes some way towards explaining why hexagons:

* "minimize the quantization error introduced when users move through a city"

* "allow us to approximate radiuses easily"

* non-hexagonal regions (such as postal code boundaries) "have unusual shapes and sizes which are not helpful for analysis, and are subject to change"

</comment><comment><USER11> >Hexagons are just pentagons without one side

My favorite quote in the video

<comment><USER12> Don't they have one more side?

<comment><USER13> They do.

</comment></comment></comment><comment><USER14> How does this compare to S2 from google? It is not mentioned in the post at all.

[http://s2geometry.io/](http://s2geometry.io/)

<comment><USER15> You get more aesthetic visuals from H3.

S2 cells distort quite heavily depending on which part of the globe you're mapping.

<comment><USER16> I think this is the real answer. I've like hex tiles for a long time, but they don't nest properly like squares in a quadtree. I think someone at Uber decided to "make it work" because it looks cool. They traded one set of problems for another, and I think from a technical point of view they made a poor choice.

<comment><USER17> > I think from a technical point of view they made a poor choice.

based on what criteria? H3 vs S2 is a tradeoff.

<comment><USER16> >> based on what criteria?

Well for one, the fact that they don't nest properly. They mention that you can get the address of the parent hexagon by truncating that of the current one. The problem is that doesn't actually work all the way up because certain tiles on the border will flip back and forth in strange ways. They had to do something to deal with this, just like the would have had to do something else with squares having two kinds ot neighbors. The squares issues are more obvious though and the code to deal with it will probably be very localized.

I mean, don't make a nested spatial index with spacial regions that don't actually nest. The structure fails at its primary claim.

<comment><USER18> Agreed,it seems incomprehensible that you would accept such nesting problems.

</comment></comment></comment></comment></comment></comment><comment><USER19> Thread from last year: [https://news.ycombinator.com/item?id=17417545](https://news.ycombinator.com/item?id=17417545)

</comment><comment><USER20> If anyone wants to use this in R, the h3-r package works quite nicely. It's in C which, in my tests, is an order of magnitude faster than the v8 implementation. We use it to chop up spatial data into equally sized chunks that we can use as observations for regressions and the like. [https://github.com/crazycapivara/h3-r](https://github.com/crazycapivara/h3-r)

</comment><comment><USER15> I work for a delivery company. We currently use H3 to help calculate ETAs in realtime.

<comment><USER21> Does that work? I'd expect you want to do a fairly traditional road-based ETA? Otherwise you'll be wildly off if you're in a cul de sac next to a major highway or on said highway, or in massive traffic vs not at all.

<comment><USER15> It's more to figure out how many couriers are in a given cell at a given time, and track that data over time so it can be forecasted.

Then we can say if you need a package collecting at address X, there are usually Y available couriers within Z distance. Combine that with a road mapping/traffic API and you're done.

</comment></comment></comment><comment><USER22> I hate Uber, but I now opened this issue suggesting a way to massively increase the performance of this anyway:

[https://github.com/uber/h3/issues/258](https://github.com/uber/h3/issues/258)

(Note: by "massively" I mean pushing it to O(1) for the fundamental coordinate operations. So, perhaps read that as "most massively".)

</comment><comment><USER23> I might be the only one pedantically annoyed here, but... the very first image on this page contains a mix of hexagons and pentagons.

Which is it - an inaccurate image, and the system is really hexagon-based, or does the system also use pentagons? My guess is that it is actually all hexagon-based since the overlap between granularity is already only approximate.

</comment><comment><USER24> Is UberCon going on or something? Why so many releases in the past few days? I'm not complaining; just curious.

<comment><USER25> This article is over a year old.

</comment></comment><comment><USER26> I wonder why healpix from NASA wasn't an option for them. Maybe the nonpermissive license...

</comment><comment><USER27> Why does each cell contain seven finer cells instead of six, resulting in imperfect containment?

<comment><USER28> You can't divide a hexagon into 6 regular hexagons, that would mean using triangular cells to subdivide the hexagon.

Which isn't to say that you _couldn 't_ tile the planet with triangles, but they point out that the consistent relationship between neighboring hexagon tiles is useful:

 _> Using a hexagon as the cell shape is critical for H3. As depicted in Figure 6, hexagons have only one distance between a hexagon centerpoint and its neighbors', compared to two distances for squares or three distances for triangles. This property greatly simplifies performing analysis and smoothing over gradients._

As you noticed, you can't divide a hexagon into 7 regular hexagons either. But it's apparently close enough:

 _> H3 supports sixteen resolutions. Each finer resolution has cells with one seventh the area of the coarser resolution. Hexagons cannot be perfectly subdivided into seven hexagons, so the finer cells are only approximately contained within a parent cell._

<comment><USER27> Thanks! It turns out I am bad at hexagons.

</comment></comment></comment><comment><USER29> There's a lot to be said for a hexagonal grid. I looked at this once for a collision detection system. It's convenient to get rid of the special cases needed where four cells meet. You have to invent some new bookkeeping, but it can be worth it.

<comment><USER30> The aliasing / moiré artifacts are also dramatically less objectionable with hexagonal grids.

Now that image sensors and e.g. smartphone displays are very high resolution, and most content ends up going through multiple resampling routines on its way from capture -> storage/processing -> display, I would love to see people start to experiment with hexagon-grid cameras and displays. The slightly more complicated resampling wouldn't really be a big deal for modern DSP hardware, and the visual output could be significantly better for the same pixel count.

</comment></comment><comment><USER31> I love the aesthetics of hexagons.

It should be possible to turn this projection into quite a nice 3D printable model. Challenging, though. Probably one could try to split the sphere into equal hexagons for printing and then assemble.

<comment><USER32> You can't make a sphere entirely out of hexagons; the math doesn't work [1]. In the article they note that they include 12 pentagons too, to solve this problem. Neatly, they arrange to have all the pentagons in areas of water where they presumably won't have to analyse traffic patterns for a while.

(I mention it mostly because I think it's an interesting little mathematical factoid.)

[1] [https://math.stackexchange.com/q/2121175](https://math.stackexchange.com/q/2121175)

<comment><USER30> One thing you can do though is tile an octahedron by just hexagons. At each of the 6 corners you end up with 2 hexagons which border each-other along 2 edges (instead of the usual 1). If you blow this octahedron up into a sphere those hexagons appear to be pentagons, because two of their edges are colinear (i.e. the same great-circle arc).

This can be nicer in some cases: the edge case your hexagon-grid algorithms have to deal with is having a hexagon with one of the same neighbors twice, instead of needing to worry about pentagons per se.

<comment><USER33> Would you care to explain this? When you mention tiling an octahedron with hexagons, the first thing I imagine is a truncated octahedron, which is composed of hexagons and squares.

<comment><USER30> You can start with 4 hexagons, each one covering an octant and a third of the neighboring octants.

Or another way to say this: if you start with 4 hexagons, with each glued together with each other along two adjacent edges, and you add the appropriate folds, you can make an octahedron.

Then you can subdivide each of those starting hexagons into _n_ hexagons for any of these numbers, [https://oeis.org/A003136](https://oeis.org/A003136) (power-of-4 sizes may be the most convenient among these, so that the overall grid has 2^n by 2^n size)

</comment></comment></comment></comment></comment><comment><USER34> Python bindings on Windows working yet?

<comment><USER15> David Ellis is working on this [https://github.com/dfellis/h3-py/pull/1](https://github.com/dfellis/h3-py/pull/1)

</comment></comment><comment><USER35> Second time seeing it, would love to use it just for fun, but no idea what to do

</comment><comment><USER36> Utterly Brilliant!

</comment><comment><USER37> H3 is working for the specific Ubers' needs. Not much useful as S2.

<comment><USER3> Could you give more details? After reading the article I think the main reason is the subdivision algorithm which for S2 is easier but for everything else hexagon seems like a better approach.

<comment><USER38> Subdividing tiles can be more important than everything else: knowing in which tile a point lies is a fundamental operation for a spatial indexing system and it has to be very easy and efficient.

<comment><USER4> It's also vital for correct aggregation: if you sum up some quantity over all the subdivisions of some area, you really want that sum to be equal to the quantity in that area. With this hexagonal pseudo-subdivision, it isn't.

<comment><USER3> I think as long as you're adding the leaves on the same resolution level it should be fine. the problem is when your storing objects in different levels as it would be possible on a KDB tree.

</comment></comment></comment></comment></comment><comment><USER39> did not look at the code yet, but the algo for subdiving might be a nightmare.

square and triangle are weird for distance, maybe. but they can all hold precise subdivisions of the shape inside each other. hexagon "bleed", so why exactly they boast so many times in the article that h3 is so great for nesting different details levels? even their diagrams show very bad bleeding (worse than it should be if optimized) and they never mention it on this summary.

</comment><comment><USER40> Beautiful blog post!</comment>


Open Source Networks and Heroin - <AUTHOR> http://globalguerrillas.typepad.com/globalguerrillas/2010/02/journal-open-source-networks-and-heroin.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+typepad%2FrzYD+%28Global+Guerrillas%29 <comment><USER2> So they compared their methods with each other. It seems like too broad a definition of "open source" to me. Interesting article otherwise.</comment>


Two Teeny Tiny Fonts - <AUTHOR> http://www.sitepoint.com/blogs/2009/09/22/two-teeny-tiny-fonts/

<comment><USER2> At the other (and more preferable) end of the solution: What current technology offers the most pixels per square inch? How far away are we from a 1080p PDA/smartphone screen?

<comment><USER3> LCD Projectors fit 1080p in ~0.75" diagonal for roughly 3000 pixels per square inch. That seems to be roughly the limit of our technology.

<comment><USER4> As a side note 4x 1080p projectors fit with that assumption.

 _The 4K resolution of the new panel, which measures 1.64-inches diagonally, translates to 8.85 megapixels and is four times the resolution of full HD_ <http://www.gizmag.com/epson-2160p-lcd-projector-panel/13333/>

</comment></comment></comment><comment><USER5> Subpixel Abe Lincoln <http://www.michaelbach.de/ot/fcs_mosaic/>

<comment><USER6> Why blur the serial number on the money? Is someone really going to find the bill, notice it has cocaine on it, and blame the author of the blog post?

</comment></comment><comment><USER7> Work amazingly well. Is there a barrier to this being available as an ordinary font?

> In contrast, I've noticed that Microsoft's smallest screen fonts are > unreadable, whereas their smallest readable screen fonts are way bigger than > necessary. "

Interesting, given ClearType (an example in "Microsoft's Creative Destruction" <http://news.ycombinator.com/item?id=1100377>): "It worked by using the color dots of liquid crystal displays to make type much more readable on the screen"

</comment><comment><USER8> I've yet to find a download link for the first font "The Bee's Knees".

<comment><AUTHOR> The original and best: <http://minifonts.com/mini7.html>

But not as small, of course.

<comment><USER9> I find Silkscreen to be the tiny-font of choice.

And it's free: <http://kottke.org/plus/type/silkscreen/>

</comment></comment></comment><comment><USER10> BTW, if you want to quickly see how this text looks on an iPhone, etc, I made a shortlink direct to the demo image so it's easier to type on there.. <http://bit.ly/tinytext>

<comment><USER11> Note that as it relies on subpixels it'll only work as intended in one orientation on iPhone.

<comment><USER10> This is something that's bugging me about the iPad. Since the screen is 1024x768 (and TFTs are typically manufactured in portrait), I wonder if the pixels are oriented vertically rather than horizontally when you're in portrait mode. If so, the font rendering for books could be horrible compared to if you had it in landscape.

Anyone got any ideas/insight on this?

<comment><USER12> Would it be possible in the future to supplement our existing font formats to have two versions, one for subpixels one way, and one for the other (so that the OS could transparently switch between which version to use)? Or am I misunderstanding how subpixel fonts work?

<comment><USER13> That depends on if it's a bitmap font or not. If it is bitmap, then it's already subpixel rendered, and you would need two different bitmaps depending on orientation. If it's truetype or similar, you would need a font renderer that was capable of subpixel rendering, and it would then have to render it differently depending on orientation.

However, subpixel rendering works because you effectively triple the _horizontal_ resolution. If you flip your screen, you now have normal horizontal resolution, but triple the vertical resolution, which is less useful for rendering fonts, and it would of course also not look the same as the horizontally subpixel-rendered font.

So for devices like that, it's probably best to simply not do it and get a dense enough display that you won't need it.

Also, does anyone know if subpixel rendering works on OLED screens?

</comment></comment></comment></comment></comment><comment><USER14> If nothing else, be sure to check out the Ken Perlin's homepage (he's the guy behind the second font). <http://mrl.nyu.edu/~perlin/>

</comment><comment><USER15> That second font was created by Ken Perlin, of Perlin Noise fame.

<http://news.ycombinator.com/item?id=1105632>

</comment><comment><USER10> If we could render Hacker News with this system, think of how many more stories we could get on the front page. I vote Aye.

</comment><comment><USER16> How well, if at all, do these fonts scale upwards?

<comment><USER17> It's a bitmap font, so it scales as any pixels would but far from well when it comes to readability. If you look at the 1600% up-scale you get a good idea what I am talking about.

I remember making these types of fonts myself back in the Amiga days just to fit it on bootsector(s) (memory fails me here, was it one or two?). The difference then was that sub pixel rendering was not an option, and fixed width fonts at this size always looked bad (i vs m), so you'd have to be careful how you wrote things. :-)

Without having ever experimented with subpixel rendering I am intrigued by the fact that « is made a whole lot more "blue" than » -- spontaneously one would think it would simply be a matter of mirroring the glyphs (obviously not) :)

<comment><USER18> If you want to experiment with subpixel rendering, and you have a reasonably modern Firefox, I made a subpixel-rendering toy a while ago: <http://zork.net/~st/Toys/subpixel-sketch.html>

If you don't have a modern Firefox, there's a screenshot here: <http://zork.net/~st/Toys/subpixel-sketch.png>

<comment><USER19> That's neat, but I wish I could click and drag to change multiple pixels at once, instead of clicking and clicking and clicking.</comment></comment></comment></comment>


Show HN: Problem Hunt – Discover a startup idea that actually solves a problem - <AUTHOR> http://www.probhunt.com <comment><USER2> ...more millenial problems? The real version of this is Code For America, which embeds devs with govs. Get the problems from people outside tech.

<comment><USER3> Meaningful global problems, even, not just coffee and bicycles.

Managing water. Tracking disease and promoting vaccination. Tracking government corruption. Funding nonprofits. Modernizing education. Etc x 100. These aren't even third world problems any more.

<comment><AUTHOR> Great points, but I think all of those problems seem incredibly difficult to solve as a new entrepreneur. I guess our service is more about the "lower hanging fruits" for right now

<comment><USER2> I think that's weak minded bullshit. Aim higher.

</comment></comment></comment></comment><comment><USER4> The main problem seems people do not know the many solutions that already exist. For example from this weeks ProblemHunt:

1\. But I only got an appetizer... Going out to eat with friends is fun, but splitting the bill sucks. Either someone doesn't have cash or the person who just got an appetizer ends up paying the same amount as everyone else.

A quick google gives a ton of solutions, like: splitabill.com kittysplit.com [https://itunes.apple.com/us/app/splitwise-split-bills- expens...](https://itunes.apple.com/us/app/splitwise-split-bills- expenses/id458023433) [https://play.google.com/store/apps/details?id=com.msafiullah...](https://play.google.com/store/apps/details?id=com.msafiullah.splitbill) [http://techcrunch.com/2015/05/03/split-lets-you-split-the- bi...](http://techcrunch.com/2015/05/03/split-lets-you-split-the-bill-fairly- not-equally/)

2\. Anyone got a charge? I love riding my bike while using my phone for its GPS, but using the GPS completely drains my battery. By the time I get to my destination my phones dead!

In Europe it would be no problem to charge your phone in most coffee shops, bars or restaurants. In Asia they even advertise with 'free phone charge' (or they put a price on it). But maybe I misunderstand the problem and is it more specific ? There are also portable battery chargers in all sizes ?

For most of the other problems it would not be difficult to find an existing solution either. So this could be an idea for monetization: have people set a reward for solving their problem. In relation to how big the problem really is to them ? I will then gladly solve the 'low hanging fruit' :-)

Edit: typing error

</comment><comment><USER4> Another possible improvement: people should describe a possible ideal solution as well. The problems now seem easy to solve but maybe its only because the description is too vague.

<comment><AUTHOR> Interesting idea. My only bone to pick with solutions is that I think it actually puts a limit on creativity. When you have a completely open ended problem I think it sparks a different mechanism in your brain than when you see a solution presented for you. Another thought I had was to maybe do less problems per week, but really break down what's going on in each problem and viewing the problem from multiple perspectives. Curious what your thoughts are on that?

<comment><USER4> 'My only bone to pick with solutions is that I think it actually puts a limit on creativity'

I understand. That is true if one would use the 'problems' just as another starting point for creativity. But for that one could already read newspapers, Facebook, etc, etc. No need for these (to me) very vague problems.

'to maybe do less problems per week, but really break down what's going on in each problem and viewing the problem from multiple perspectives'

But if _you_ try to look at all angles you might miss the problem a person actually has ?

So I propose to have the person put in more effort - to push him/her into a bit more focusing. Maybe by adding some extra questions by asking for visualizing a solution. If someone does not want to think a little bit harder for a solution to the problem, then there is no real problem. So that might be a good filter as well ;-)

</comment></comment></comment><comment><USER5> One of the things that might be bad about this is competition. If I'm trying to start a startup and I've noticed a common problem and there's zero competition for solutions - that would be the ideal scenario for a new startup. But a service like this could have multiple people inadvertently working on duplicate solutions for the same problem. There is no mutex.

Don't get me wrong its a cool idea but probably nothing will beat basic observation and creative thinking when it comes to finding new ideas.

<comment><AUTHOR> That's true multiple people could be working on the same problem, but I'd counter with two points. One, MySpace came first and solved a similar problem to Facebook, yet two totally different outcomes - execution is key. And two, I think the cool thing about sending problems not "business ideas" is that one problem statement could yield a thousand different solutions.

</comment></comment><comment><USER6> How would someone go about responding to these problems? For instance, #10 on [http://www.probhunt.com/example2.html](http://www.probhunt.com/example2.html) can be solved by joining one of the many IRC channels or Slack chats that focus on the language.

</comment><comment><USER7> Interesting. I've created problems.club (I posted link to HN yesterday), because I want to find a problems, which new startupers and other people like me can solve. Your project pursues the same idea.

<comment><AUTHOR> Oh really that's interesting. Similar idea, two different approaches.

</comment></comment><comment><USER8> Or you can practice needfinding

</comment><comment><USER9> i think this is a great idea!</comment>


Amazon is shutting down its Fresh grocery delivery service in parts of 9+ states - <AUTHOR> https://www.recode.net/2017/11/3/16601488/amazon-fresh-cancellation-shut-down-grocery-delivery-whole-foods <comment><USER2> I'd like to know why they're shrinking their list of locations.

I love using Fresh, in Seattle. Saves me several hours per week; reduces the need for car trips and navigating nasty parking lots; avoids walking past aisles of bad food; and removes the headache of shopping with my young children who are tempted by every sugar-based object in sight or within reach.

On the minus side, I really dislike that they've introduced tipping (defaults to $5). Somewhat rarely, the people who bag items are thoughtless (putting fresh fruits next to ice bags; crushing yogurt with heavy items on top).

I've tried the pickup variation instead of delivery but often some items are unavailable for pickup, and it it simply very convenient to find my groceries in front of the house at 5 or 6am.</comment>


WebGL around the net, 10 May 2012 - <AUTHOR> http://learningwebgl.com/blog/?p=4852

<comment><USER2> Neat, my Fl0wer demo was featured there. That version is a bit of a WIP (it started as a quick hack in the morning to get my brain working) and weighed in at 891 bytes. The new version is at <http://demoseen.com/windowpane/nufl0wer.png.html> and is 747 bytes -- still a long way to go before it hits 512, though. I've got some nice renders of it at <http://www.behance.net/gallery/Fl0wer/3914351> as well; it's funny to think that the demo itself could fit thousands of times into any image on that page.

(I feel obligated to note that the Behance page has prints available for sale, which I'd absolutely love for you to buy; I decided to knock my cut down to 0% to bring the prices down to something I considered sane, since I really don't care about making money from it. Edit: Btw, the standard cut I'd get from one of these is about $36. If you buy a print and feel inclined to do something more, find a broke programmer and them a Raspberry Pi with the money you save.)

<comment><USER3> Saw this when it was on HN a while back - great work. Also The way you get the source is brilliant. Never seen that before. Is that your own technique?

<comment><USER2> Glad you enjoyed it. Using PNGs to compress code is an old technique, but making it one file containing everything is my own; I described everything at <http://daeken.com/superpacking-js-demos> if you're curious. I'm going to write a followup once I get Fl0wer down to 512b ;)

</comment></comment></comment><comment><USER4> Google cache:

[http://webcache.googleusercontent.com/search?q=cache:4MA6nEb...](http://webcache.googleusercontent.com/search?q=cache:4MA6nEbwuhgJ:learningwebgl.com/blog/%3Fp%3D4852+http://learningwebgl.com/blog/%3Fp%3D4852)

</comment><comment><USER5> > An interesting post on the state of the port of Sauerbraten to WebGL (from > C++/OpenGL) by Alon Zakai — no new demos, but worth reading if you're > interested in what you can do with Emscripten.

There _is_ a new demo there since last week,

<http://www.syntensity.com/static/bb/client_6.html>

is the latest (includes models with bumpmapping, FPS arms, some other stuff).</comment>