Testing effect.
(At this point, I should really know better than to trust myself to write anything at 1 in the morning.)
richard_reitz
Karma: 328
if you’ve read all of a sequence you get a small badge that you can choose to display right next to your username, which helps people navigate how much of the content of the page you are familiar with.
Idea: give sequence-writers the option to include quizzes because this (1) demonstrates a badgeholder actually understands what the badge indicates they understand (or, at least, are more likely to) and (2) leverages the testing effect.
I await the open beta eagerly.
I have taken the survey.
Extremely interested, would move anywhere rationalists would set one of these up.
When I first read In Fire Forged, I really liked it, but saw things I could improve. So, I left some high-quality reviews on fanfiction.net (that is, reviews that demonstrated I somewhat knew what I was talking about) and then solicited the author. From there, networking (people who you collaborated with can collaborate with you).
Back-engineering, I’d tentatively suggest just posting somewhere with reasonable visibility that selects for writers you’d like to collaborate as, and then ask anyone interested to ping you. Alternatively, you could develop a relationship working on someone else’s writing and then ask them to look at your’s.
You guys voted to develop Righteous Face Punching Style and add Kagome to your party. What do you need my help in decision-making for? (But, seriously, I probably shouldn’t have taken the time to get caught up, much less actively participate. Fun read, though!)
Ha! I give Lighting Up the Dark—also by Velorien—last pass editing.
Thanks for the rec. It looks really good.
Do you have any examples of pieces that were written collaboratively?
In addition to In Fire Forged (in which I did first-round micro, in addition to contributing to worldbuilding), I give a last pass micro to Lighting Up the Dark (rational Naruto fanfic). I contributed a little to the Second Secular Sermon, although verse is really not my thing. I also have a partnership with Gram Stone that includes looking over each other’s LW posts.
Do you keep a history of changes and discussions?
In Fire Forged has a Skype group, which keeps an archive of our discussion. Since Google Docs aren’t the final publishing form, you can keep comments around, although in practice, once we’ve resolved an issue, the comment/suggestion usually goes away, so things don’t get more cluttered. If you’re interested, this is the Google Doc for this piece. But Google Docs doesn’t keep a changelog, I have no desire to look back at one, nobody I’ve talked to has indicated any desire to look back at one, so there is no history of changes.
How do you determine the direction of the story, is there a single leader who makes the big decisions, or is it more egalitarian?
I more fully discussed this here, but the tl;dr is that experience indicates a single-leader setup usually works best, and is also the only setup I’ve come across. That said, it’s egalitarian in the sense that the primary author doesn’t give any special consideration to the words they’ve written or the ideas they’ve had; in the end, you want the best ideas expressed by the best words on the page. I can’t imagine the author who would pass up improvements to their creative baby just because they weren’t the ones to come up with them.
I’m sorry my title misled you.
(Since writing has trouble carrying intent: I genuinely feel bad that the title I chose caused you to believe something that wasn’t true. I wish I was smart enough to have come up with a title that more precisely communicated what I was and wasn’t discussing.)
This is perhaps a case of different projects being best served by different practices. There’s certainly nothing stopping you from making a Google Doc where two (or more) authors have editing permission (as opposed to commenting permission).
But it’s absolutely true that I’m writing from the perspective of having one primary author. This is because every piece I’ve worked on has had one primary author. Paul Graham writes: “Design usually has to be under the control of a single person to be any good.” Indeed, almost all books of fiction I’m aware of were published by one author. A quick survey indicates that even most TV shows—which have writing staffs—usually have one author, although it’s somewhat more common to have several people collaborate as equals to put together a story, which is then written up by one person. This was more or less how Buffy got written, as described by Jane Espenson.
It would certainly have been a major breakthrough if I’d discovered how to have multiple authors consistently work together to make good work. But that’s above my pay grade; if a bunch of professional writers who have been in the business for decades have a strong preference for single authorship, I see that as a strong indication that I should generally prefer single authorship.
Also, if this piece comes off as having collaborators mostly making small edits, that’s partly because it’s true, but partly my own bias. Certainly, in In Fire Forged, we had one or two people who primarily worked with the author on macro level issues (plot, characterization, thematic consistency, etc), while I worked on the micro level. But it’s also partly because it’s true; outside of two fanfics (plus a poem), I mostly work on nonfiction blog posts. In these, the author knows what they want to say and have said it, and just need to say it better. They may or may not benefit from a fact check (usually not, at least for the pieces I’ve worked on), but beyond that, most of the room for improvement comes in the form of little changes.
Lastly, I have to thank you. This is the first thing I’ve actually published. An earlier draft contained a section discussing what I’ve just said, but I cut it because I didn’t think it contained material that was useful to either author or collaborator. Obviously, I was wrong! So, now I have a slightly better sense of when cutting stuff goes too far.
Yes; Eliezer recommended it in an Author’s Note, which is how I got involved.
It’s also not dead so much as on a very extended hiatus. Our author started a computer game company and has been prohibitively busy for a while now. There’s a blog with updates about the lack of updates.
If anyone would like a collaborator for something they’re writing for LessWrong or diaspora, please PM me. Anyone interested in being a collaborator can reply to this comment, thereby creating a collaborator repository.
my classes continue to perform with increasingly minimal note-taking and homework.
Which homework hasn’t been assigned because of Anki? Remembering back to my high school English classes, the only homework I can remember doing was reading readings and writing essays. I can’t see how either could be displaced by Anki.
I have taken the survey.
And yet, humans currently have the edge in Brood War. Humans are probably doomed once StarCraft AIs get AlphaGo-level decision-making, but flawless micro—even on top of flawless* macro—won’t help you if you only have zealots when your opponent does a muta switch. (Zealots can only attack ground and mutalisks fly, so zealots can’t attack mutalisks; mutalisks are also faster than zealots.)
*By flawless, I mean macro doesn’t falter because of micro elsewhere; often, even at the highest levels, players won’t build new units because they’re too busy controlling a big engagement or heavily multitasking (dropping at one point, defending a poke elsewhere, etc). If you look at it broadly, making the correct units is part of macro, but that’s not what I’m talking about when I say flawless macro.
Excellent points; “rigorous” would have been a better choice. I haven’t yet had the time to study any computational fields, but I’m assuming the ones you list aren’t built on the “fuzzy notions, and hand-waving” that Tao talks about.
I should also add I don’t necessarily agree 100% with every in Lockhart’s Lament; I do think, however, that he does an excellent job of identifying problems in how secondary school math is taught and does a better job than I could of contrasting “follow the instructions” math with “real” math to a lay person.
I once took a math course where the first homework assignment involved sending the professor an email that included what we wanted to learn in the course (this assignment was mostly for logistical reasons: professor’s email now autocompletes, eliminating a trivial inconvenience of emailing him questions and such, professor has all our emails, etc). I had trouble answering the question, since I was after learning unknown unknowns, thereby making it difficult to express what exactly it was I was looking to learn. Most mathematicians I’ve talked to agree that, more or less, what is taught in secondary school under the heading of “math” is not math, and it certainly bears only a passing resemblance to what mathematicians actually do. You are certainly correct that the thing labelled in secondary schools as “math” is probably better learned differently, but insofar as you’re looking to learn the thing that mathematicians refer to as “math” (and the fact you’re looking at Spivak’s Calculus indicates you, in fact, are), looking at how to better learn the thing secondary schools refer to as “math” isn’t actually helpful. So, let’s try to get a better idea of what mathematicians refer to as math and then see what we can do.
The two best pieces I’ve read that really delve into the gap between secondary school “math” and mathematician’s “math” are Lockhart’s Lament and Terry Tao’s Three Levels of Rigour. The common thread between them is that secondary school “math” involves computation, whereas mathematician’s “math” is about proof. For whatever reason, computation is taught with little motivation, largely analogously to the “intolerably boring” approach to language acquisition; proof, on the other hand, is mostly taught by proving a bunch of things which, unlike computation, typically takes some degree of creativity, meaning it can’t be taught in a rote manner. In general, a student of mathematics learns proofs by coming to accept a small set of highly general proof strategies (to prove a theorem of the form “if P then Q”, assume P and derive Q); they first practice them on the simplest problems available (usually set theory) and then on progressively more complex problems. To continue Lockhart’s analogy to music, this is somewhat like learning how to read the relevant clef for your instrument and then playing progressively more difficult music, starting with scales. [1] There’s some amount of symbol-pushing, but most of the time, there’s insight to be gleaned from it (although, sometimes, you just have to say “this is the correct result because the algebra says so”, but this isn’t overly common).
Proofs themselves are interesting creatures. In most schools, there’s a “transition course” that takes aspiring math majors who have heretofore only done computation and trains them to write proofs; any proofy math book written for any other course just assumes this knowledge but, in my experience (both personally and working with other students), trying to make sense of what’s going on in these books without familiarity with what makes a proof valid or not just doesn’t work; it’s not entirely unlike trying to understand a book on arithmetic that just assumes you understand what the + and * symbols mean. This transition course more or less teaches you to speak and understand a funny language mathematicians use to communicate why mathematical propositions are correct; without taking the time to learn this funny language, you can’t really understand why the proof of a theorem actually does show the theorem is correct, nor will you be able to glean any insight as to why, on an intuitive level, the theorem is true (this is why I doubt you’d have much success trying to read Spivak, absent a transition course). After the transition course, this funny language becomes second nature, it’s clear that the proofs after theorem statements, indeed, prove the theorems they claim to prove, and it’s often possible, with a bit of work [2], to get an intuitive appreciation for why the theorem is true.
To summarize: the math I think you’re looking to learn is proofy, not computational, in nature. This type of math is inherently impossible to learn in a rote manner; instead, you get to spend hours and hours by yourself trying to prove propositions [3] which isn’t dull, but may take some practice to appreciate (as noted below, if you’re at the right level, this activity should be flow-inducing). The first step is to do a transition, which will teach you how to write proofs and discriminate between correct proofs from incorrect; there will probably some set theory.
So, you want to transition; what’s the best way to do it?
Well, super ideally, the best way is to have an experienced teacher explain what’s going on, connecting the intuitive with the rigorous, available to answer questions. For most things mathematical, assuming a good book exists, I think it can be learned entirely from a book, but this is an exception. That said, How to Prove It is highly rated, I had a good experience with it, and other’s I’ve recommended it to have done well. If you do decide to take this approach and have questions, pm me your email address and I’ll do what I can.
This analogy breaks down somewhat when you look at the arc musicians go through. The typical progression for musicians I know is (1) start playing in whatever grade the music program of the school I’m attending starts, (2) focus mainly on ensemble (band, orchestra) playing, (3) after a high (>90%) attrition rate, we’re left with three groups: those who are in it for easy credit (orchestra doesn’t have homework!); those who practice a little, but are too busy or not interested enough to make a consistent effort; and those who are really serious. By the time they reach high school, everyone in this third group has private instructors and, if they’re really serious about getting good, goes back and spends a lot of times practicing scales. Even at the highest level, musicians review scales, often daily, because they’re the most fundamental thing: I once had the opportunity to ask Gloria dePasquale what the best way to improve general ability, and she told me that there’s 12 major scales and 36 minor scales and, IIRC, that she practices all of them every day. Getting back to math, there’s a lot here that’s not analogous to math. Most notably, there’s no analogue to practicing scales, no fundamental-level thing that you can put large amounts of time into practicing and get general returns to mathematical ability: there’s just proofs, and once you can tell a valid proof from an invalid proof, there’s almost no value that comes from studying set theory proofs very closely. There’s certainly an aesthetic sense that can be refined, but studying whatever proofs happen to be at to slightly above your current level is probably the most helpful (like in flow), if it’s too easy, you’re just bored and learn nothing (there’s nothing there to learn), and if it’s too hard, you get frustrated and still learn nothing (since you’re unable to understand what’s going on).)
“With a bit of work”, used in a math text, means that a mathematically literate reader who has understood everything up until the phrase’s invocation should be able to come up with the result themselves, that it will require no real new insight; “with a bit of work, it can be shown that, for every positive integer n, (1 + 1/n)^n < e < (1 + 1/n)^(n+1)”. This does not preclude needing to do several pages of scratch work or spending a few minutes trying various approaches until you figure out one that works; the tendency is for understatement. Related, most math texts will often leave proofs that require no novel insights or weird tricks as exercises for the reader. In Linear Algebra Done Right, for instance, Axler will often state a theorem followed by “as you should verify”, which should require some writing on the reader’s part; he explicitly spells this out in the preface, but this is standard in every math text I’ve read (and I only bother reading the best ones). You cannot read mathematics like a novel; as Axler notes, it can often take over an hour to work through a single page of text.
Most math books present definitions, state theorems, and give proofs. In general, you definitely want to spend a bit of time pondering definitions; notice why they’re correct/how the match your intuition, and seeing why other definitions weren’t used. When you come to a theorem, you should always take a few minutes to try to prove it before reading the book’s proof. If you succeed, you’ll probably learn something about how to write proofs better by comparing what you have to what the book has, and if you fail, you’ll be better acquainted with the problem and thus have more of an idea as to why the book’s doing what it’s doing; it’s just an empirical result (which I read ages ago and cannot find) that you’ll understand a theorem better by trying to prove it yourself, successful or not. It’s also good practice. There’s some room for Anki (I make cards for definitions—word on front, definition on back—and theorems—for which reviews consist of outlining enough of a proof that I’m confident I could write it out fully if I so desired to) but I spend the vast majority of my time trying to prove things.
It has happened more than once that a professor has assigned a textbook, which I bought, only for the professor to say in the first class that the only reason they assigned a textbook is because they were required to, but will never use it. Holding off on buying textbooks until after the first class (or, I guess, emailing the professor to ask if they plan on using the textbook) would have saved me several hundreds of dollars. (Having textbooks to study from is nice—they are, to me, the most efficient way of getting up to speed in math or science—but the ones professors assign because they need to put something down tend not to be the best ones.)
Lemma: sum of the degrees of the nodes is twice the number of edges.
Proof: We proceed by induction on the number of edges. If a graph has 0 edges, the the sum of degrees of edges is 0=2(0). Now, by way of induction, assume, for all graphs with n edges, the sum of the degrees of the nodes 2n; we wish to show that, for all graphs with n+1 edges, the sum of the degrees of the nodes is 2(n+1). But the sum of the degrees of the nodes is (2n)+2 = 2(n+1). ∎
The theorem follows as a corollary.
If you want practice proving things and haven’t had much experience so far, I’d recommend Mathematics for Computer Science, a textbook from MIT and distributed under a free license, along with the associated video lectures *. To use Terry Tao’s words, Sipser is writing at both level 1 and 3: he’s giving arguments an experienced mathematician is capable of filling in the details to form a rigorous argument, but also doing so in such a way that a level 1 mathematician can follow along. Critically, however, from what I understand from reading Sipser’s preface, he’s definitely not writing a book to move level 1 mathematicians to level 2, which is a primary goal of the MIT book. If you’re looking to prove things because you haven’t done it much before, I infer you’re essentially looking to transition from level 1 to 2, hence the recommendation.
A particular technique I picked up from the MIT book, which I used here, was that, for inductive proofs, it’s often easier to prove a stronger theorem, since it gives you stronger assumptions in the inductive step.
PM me if you want someone to look over your solutions (either for Sipser or the MIT book). In the general case, I’m a fan learning from textbooks and believe that working things out for yourself without being helped by an instructor makes you stronger, but I’m also convinced that you need feedback from a human when you’re first getting learning how to prove things.
* The lectures follow an old version of the book, which ~350 pages shorter and, crucially, lacks exercises.
It helps to explicitly visualize people who I perceive as being skilled in X failing at it over and over again
Some of the greatest value I’ve gotten out of attending math lectures comes from seeing math Ph.Ds (particularly good ones) make mistakes or even forget exactly how a proof works and have to dismiss class early. It never happened often, but just often enough to keep me from getting discouraged.
If I’m understanding you correctly, you don’t think people who can’t individually affect the equilibrium are evil? Scientists who would be outcompeted, and therefore unable to do science, if they failed to pursue a maximally impressive career seem an example of this. If they’re good (in terms of both ability and alignment), there’s some wiggle room in there for altruism when it’s cheap, but if err too far from having an impressive career, someone else, probably someone not making small career sacrifices for social benefit, gets the attention and funds instead, thereby reducing the total amount of good being done.
I’d be interested in some concrete examples of appealing to people’s conscience getting us less-bad equilibria so I can better understand what you’re getting at. Is the scientists who all resigned from the board of an Elsevier-owned journal and started their own an example?
Also interested in your thoughts where we’re in a suboptimal equilibrium that we’re trying to get out of and there’s 2+ optimal ones (in the sense that there’s no other equilibrium which is a Pareto improvement), but each competes with the other. For instance, suppose it’s several years ago and we agree that it’s better that gay couples have the same right to legal marriage as straight couples, but the two better equilibria are (1) elimination of marriage as a legal institution and (2) extension of marriage to gay couples, which is good for gay couples who want the legal benefits of marriage and less good for those who don’t want marriage but suffer from e.g. less favorable tax treatment. (I’d really like a better example for this, especially after the examples EY gave, but lack a large, responsive group of fb followers I can get to brainstorm examples for me.)