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In the book The Heart of Mathematics by Edward Burger and Michael Starbird, there is a quotation of a translated passage from Proclus, a 5th-century AD philosopher:

"It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is forever beaten by the waves."

I don't think I've ever seen an actual technical paper on the front page of Hacker News. I remember trying to post some of my favorites when I first came to HN, but people rarely responded to or upvoted them. Also, it's a lot more work to read a technical paper than most forms of online writing, and I hope that this new one has a much slower pace than Hacker News.

This is a good niche to try and fill. Thanks.

Security updates like this are somewhat frustrating (disclaimer: I am a fan of full disclosure, at least after the exploit is patched). If it is able to somehow glean your Twitter password from you clicking on the link, that is a serious security risk. If users voluntarily enter their username and password, there's hardly anything one can do about it, except warn users not to enter such sensitive information haphazardly.

However, I don't understand how a strong password would help in either case. Perhaps I'm overlooking another fairly obvious scenario.

Amazon S3 is actually relatively expensive. It's far cheaper in the long run to host it on your own server. However, if you don't have experience setting up scalable systems, tuning your configuration, or do not want to spend time doing that type of sysadmin stuff, it can be a good way to save time. It's like buying Coke at a vending machine instead of at a wholesale store. You're paying for the convenience more than anything else. Just be aware of how much you're being marked up.

Thanks. Now I think I understand. I guess it would be the difference between, say, a session musician or your average member in an orchestra versus a rock band trying to make it big.

However, if you focus on how you get paid rather than the cost of marginal increase in the big-picture sense, are there any purely scalable careers? Every scalable job has parts where you need to be present, from writing books to writing code. Clearly skills like writing well and proficiency in coding can work for most multiple jobs; you can just as easily be a journalist instead of nonfiction writer, for example.

Regardless, it feels great to be able to code. It's something I love to do, and can take different forms with every job. Sometimes, life is just good.

First, it's Grigori (Григорий) or "Grisha" for short. Secondly, there's quite a few mathematicians that have that look. I remember a funny story one of my professors told me about Campus Security not allowing him into a building because they thought he was a homeless person trying to get some food, before another professor called out his name and explained that he was, in fact, an eminent professor in the Math department.

That said, I sometime feel this way when I run into a professor on the BART or something. "Doesn't anybody realize they're in the presence of a genius?"

No way. It's not just a matter of people liking to listen to both Kanye West and Sufjan Stevens. I do like people listening to different types of music, but I don't think this is something that you can just attribute to "trendinesses" of pop music.

Reducing dynamic range is a problem. Try and listen one of the albums notorious for overcompression, like Red Hot Chili Pepper's Californication. You get "tired" listening to the music at such a high level of compression and volume, and the dynamics prevent the songs from having the impact that they could have. For example, on that album, the track "Parallel Universe" has essentially no change in volume between the verse and chorus and so the whole song sounds hollow and empty through a good pair of headphones or speakers, yet it sounds great live (even on tape). The songs sound fine if listened through cheap iPod earbuds or the radio, but if the album sounds exactly the same on the radio and in a home CD player, I think there's something wrong there.

The problem is that if it takes overcompression and loudness to get people to notice your music, music will continue to become louder and more compressed. If only those songs get peoples' attention and get radio play, pretty soon every song you hear will essentially have the same volume. That's not only terribly limiting to the artist, but a disservice to the fans who listen to the music.

Now, most music producers are aware of this and take pains to make a good mix, but raising awareness about this certainly would help stop this process in much of commercial music, especially as recorded music gets more popular.

I think there's a difference between hip-hop music and rock music, though. It's less important for hip-hop to have the dynamic range because the majority of its emotional expressiveness comes from the words, rhythm, the way they interact and the changes thereof. This is why having a great beats is so important and so good producers attract a lot of attention (e.g. Neptunes, Dre). Volume is not as important a factor. You really only need two levels of dynamics: one for the verses, one for the chorus/hook.

On the other hand, I think changes in volume are more important for expressiveness in rock music, for instance, in an unexpected bridge just when you feel the song is about to end. Now, most bands these days seem to compensate by having simpler dynamics, but I think it would be nice for them to have more options.

Also, wouldn't it be easier to have a good mix now that we can do most of these things on the computer instead of having to manually twiddle knobs and overdub live?

I'm not sure I follow your reasoning. Rock bands are scalable careers. They don't get paid a wage, and the income between the top performers and the mass of wannabes is huge. Being physically present is not a necessary nor sufficient condition for non-scalability. To serve a marginal customer, rock bands essentially don't have to do anything, but doctors need to put in time for the new patient.

Somehow, I don't think that most of the consumers of music products are in their early teens. Electric guitars, amps, and guitar pedals are expensive, and I doubt most teens have that kind of disposable income. I went to high school in a pretty affluent suburb, and even kids playing in bands there rarely had anything but entry-level guitars and a couple of cheap $40 pedals.

From my limited experience (working in a record store, giving guitar lessons, touring with a band), the biggest purchasers of these items seem to be men in their 20s and middle-age married men with kids trying to recapture some of their youth or introduce their children to music they love.

That said, I'd like to see where Zed buys his pedals (guitar center?), because most of pedals that I've seen have pretty tame names, like the popular Korg series of effects pedals, or technical names, like Behringer CL9 or Boss AD3. The only one that I use that come close to what he describes have been ones from Death by Audio, and they're so great that I don't mind the funny names.

Some schools already do something like this. For instance, I know that Brown does not have pluses or minuses, and they only have grades of A, B, C, and NC (no credit). Furthermore, the NC grades do not appear on official transcripts. On top of that, you can take almost any course Pass/No-Credit with an option of a written evaluation instead of a grade.

On top of that, you don't even an ocean to measure the Earth's circumference. Eratosthenes of Cyrene (born in the 3rd century BC) calculated the circumference of the earth fairly accurately using the angle of elevation of the Sun measured from two different cities. Note that implies that a round earth was common knowledge to the Greeks even at this date.

I don't understand why there's so much hate for Microsoft. There's much more to Microsoft than just Windows, Office, and Live Search. For one, I'm impressed by some of the stuff coming out of Microsoft Research that was shown at Techfest 2009, their internal research conference, in the last couple of days: [http://research.microsoft.com/en-us/events/techfest2009/vide...]

Perhaps somebody would have discovered hyperbolic or other non-Euclidean geometries before Lobachevsky? Through the lens of modern mathematics, non-Euclidean geometry seems like such a simple extension/modification of Euclidean geometry, yet it was only explored and developed in detail in the early 19th century.

To most mathematicians, valuing intuition is not a new idea. While one of the most distinguishing qualities of mathematics is its rigor, to focus on this quality misses the big picture. Henri Poincare, arguably the greatest 20th century mathematician, said it best: "It is by logic we prove, it is by intuition we invent." This theme is echoed in many of his writings about creativity in mathematics.

Turing's argument is beautiful and elegant, undoubtedly one of the gems of modern mathematics. However, the reason you don't see the intuition behind Turing's argument taught is that there is too much material to cover in a general theoretical computer science course. You need to be able to master the known material, to stand on the shoulders of giants, to make new advances in the discipline. This may not necessarily be the best way to encourage creativity and insight in computer science, but the hope is that interested students will delve deeper (like the author) and discover insights for themselves.

Lastly, at least among many mathematicians, Turing may be up there with Euclid among the demigods of mathematics, but there are those that lie still higher, people like Gauss and Euler who have yet to be matched in terms of mathematical output and impact.

My pet theory is that playing a musical instrument is less common a hobby among programmers now than it was a generation ago, because now programming tends to be associated with "Computer Science" as its own discipline, rather than a subdiscipline of math.

Near the end of this interview [http://tex.loria.fr/historique/interviews/knuth-clb1993.html], Don Knuth says that one way CS graduate students have changed since the 70s is that they are less interested in music:

"What changes have you seen in the students coming into the computer science program over the years?"

"Knuth: There is a very profound change that I can't account for. In the 70s, the majority of our students were very interested in music. The first thing we'd ask them when they came in was 'What instrument do you play?' We had lots of chamber groups and so on. Now almost none of the students are interested in music. I don't know if it's because a different kind of people are enrolling in computer science, or because it's true of all today's students, or what. If you ask computer science students now what their hobby is, the chances are most of them will say 'Bicycling'. I recently had one who played a harmonica, but there were almost no musicians in the group."

Actually, the Mandarin shi can also used for predication with the "noun shi adjective de" grammar pattern. For instance, you could say "ta shi hen gao de," for "he is very tall." This is grammatically correct, but then the sentence has a tone that is like passive voice in English. Thus, in most simple cases, like the above example, you would opt for the terser "ta hen gao" instead.

There's also a nice pdf version here: http://www.changethis.com/6.HowToBeCreative

I haven't been to noisebridge (yet), but from the people I've talked to at relatively large events like SuperHappyDevHouse, there's a quite a few smaller, informal groups of hackers getting together to work on stuff. It's just that most of these occur in peoples' apartments, so they're not open to the public. If you're interested in finding some place like this, though, I recommend you try and meet people somewhere like SHDH.

If you're in the East Bay, there's Berkeley Coworking (http://www.berkeleycoworking.com/) near the Ashby BART station. It's not all techies, and not open all the time, but it's a damn good place to get some work done.

It certainly depends on what you're interested in. This is more of an encyclopedia of mathematics than a textbook. If you want an broad idea of many different fields of mathematics and the history behind them, presented in a well-written and relatively elementary style, this is the book for you. However, the problem with being relatively elementary is that most of the articles merely skim the surface of whatever subject they are describing.

If you want to actually be able to solve problems using math (the fun part, for most amateur mathematicians), a textbook would be a better bet. If you stopped math at business calculus and want a great introduction to the calculus that mathematicians use, I wholeheartedly recommend Michael Spivak's Calculus as a next step.

This is a very insightful article, and I'm impressed with how much work the author put into getting something onto the front page of digg. If I were looking for somebody to do effective online PR, I'd be looking for somebody like this.

I think it's somewhat sad that digg is so huge now that it takes so much effort to get people to pay attention to an interesting link, and I'd be interesting in seeing if there were any way to counteract the user fragmentation that occurs as a social news site gets popular. Reddit-like categories seem to be one solution, but it seems more like a band-aid than a total solution.

I have a suggestion for what to read: the posts that make up Joel Spolsky's Introduction to Best Software Writing I. [http://www.joelonsoftware.com/articles/BestSoftwareWriting.h...]

Most of the entries included in the book are solid articles, but most tend to merely skim the surface of the topic at hand, and I would love to go deeper and discuss the posts with the HN community.

They are brief enough to have something like one per week, and not distract too much from our day jobs (no more than HN itself, anyway). Also, I believe all the entries are still freely available at their original sites, so we don't have to worry about people not participating because they could not find the book.

As for downsides, I think a couple of the posts were submitted to HN before, but I think most, if not all, of them are worth revisiting. Also, it could be the case that many members have already read the book, but again, I think these posts are good enough to read again and discuss.

When I first moved to the Bay Area, my roommate told me that the best way to find good places to eat and drink was to go onto a foodie forum like Chowhound and say something along the lines of "At [X], I had the best [Y] I've ever had!" because before you know it, you would have dozens of responses saying how wrong you were and among those responses, you'd find the best places to get [Y].

Is this trolling? Probably. But now I have an extensive list of great Bay Area eateries.

What you say in your last statement is true and helps to clarify a subtle point. I tend to shove all of that stuff (logic, set theory, problems of undecidability, etc) into the nondescript box labeled "philosophy of mathematics." When I meant a field was "small," it was not meant to be pejorative. Philosophy of mathematics is a rich and productive field with many applications within its varied fields. The main problems I see are the ones described the article I linked, in that people attempt to apply the theorems to things like physics, politics, law, or postmodern philosophy.

Of course Goedel's theorems do not totally exist in a bubble that only contains arcane mathematical incantations. For instance, Goedel's theorems imply (like the halting problem) that you cannot create a compiler that would be able to determine whether a program will not terminate and reject it, by considering what happens when you feed it a Goedel statement. However, this problem is something that I would also classify under "philosophy of mathematics."

Also, I hope I did not provide any implication that my view (or any view, for that matter), is the final word on the subject. I'm not dead-set in my own beliefs on incompleteness and if you can provide a convincing argument of a rigorous, nonmathematical application of Goedels theorems, I'd be more than happy to change my mind.

There is considerable discussion as to what exactly the incompleteness theorems imply, and there are many eminent minds on the many different sides of the argument. For instance, I believe Stephen Hawking is somebody who believes that physics cannot ultimately be formulated into a final number of finite principles. Do I believe this to be a rigorous application of Goedel's incompleteness theorems? No. Do I believe that this can be applied to fields outside a relatively restricted problem space? No. Does this mean I'm right? Of course not.

As to your point about Strong AI, I don't want to open that can of worms in this thread. I'm not yet convinced that the human mind is equivalent to any finite state machine, so I'm afraid that we don't even agree upon its the basic premises. However, I would love to discuss it any time outside of the thread.

I rather enjoyed the book, but it is largely because I knew what I was getting into. It's a pop science book, written by a person with a philosophical background, and embellished in the Hollywood-esque fashion, pitting the good guy--Goedel, the misunderstood genius--against the bad guy--Wittgenstein and the logical positivists--in a no-holds-barred showdown of ideas that lie at the heart of all truth and mathematics!

Obviously, it's a stretch at times, and there a good deal of rigor lost, but it's a pretty juicy story. If I wanted a biography, I would read one specifically about Goedel, and not one about Incompleteness. If I wanted to learn about the theorems themselves, I would pick up a copy of his paper or one of the many readable expositions of his work. But I wanted a fun read that explained why so many philosophers and nonmathematicians were interested in this rather esoteric bit of mathematics, and I certainly got that from the book.

Nonetheless, if you want a better book by the author, I recommend The Mind-Body Problem over this one.

This is exactly the kind of thinking that the article argues against. Remember that Goedel is speaking within the context of formal systems, so there is relatively little impact to any area outside of the small field of philosophy of mathematics. Anybody who tries to extrapolate beyond those bounds is either mistaken or misled as to what Goedel's incompleteness theorems actually imply. There is a much more thorough and eloquent explanation in the following link. [http://www.ams.org/notices/200604/fea-franzen.pdf]

Hell, even Einstein, who was close friends with Goedel and familiar with the result, was searching for a more fundamental physical theory than quantum mechanics, so clearly he did not believe it was a lost cause.

Playing with Lua is a blast. I don't have much experience in using it for anything but a third-order language (e.g. writing programs that write programs), but it's very lightweight, fast, and easy to pick up. I view it as a language that I use when I need the power of a programming language (as opposed to a one-off program), but not enough to justify using Perl/Python/Ruby.

There are some parts that I did find annoying, however, like the fact that in the standard libraries array indexing starts at 1 instead of 0 and that it gets a bit kludgy when you try and add lots of things that are not part of standard language features, but nothing you can't overcome.

There are a slew of fascinating recent advances in CS and I discover more with every passing semester, but for brevity I will pick three things that have been occupying my mindspace as of late.

1. It seems that lazy functional programming languages (like Haskell) may provide a basis for a serious improvement in more robust natural language processing. A survey paper: [http://cs.uwindsor.ca/~richard/PUBLICATIONS/NLI_LFP_SURVEY_D...]

2. Semi-Human Instinctive AI, a new dynamic, nondeterministic decision-making process, seems to be the new hotness in robotics/learning algorithms. In it, a given agent is given a set of basic behaviors ("instincts") that it hones with both open and closed learning methods in a problem space. [http://en.wikipedia.org/wiki/Semi_Human_Instinctive_Artifici...]

3. Anatoly Shalyto's Automata-based programming, using finite state machines to describe program behavior, seems to have a lot of potential. It attempts to view programs from the context of engineering control theory, which opens the door to the use of powerful techniques from dynamical systems in mathematics.

Why argue with the MIT folks? Because even MIT changed its intro programming class's language from Scheme to Python.

That said, I would still have liked to learn Scheme or a Lisp as a first language. It's a tiny language at its foundations and allows you to express many different computer science concepts with little effort. Also, it's much, much easier to write a Scheme interpreter in Scheme than a Python interpreter in Python.