Once upon a time, in a lonely little village, beneath the boughs of a forest of burning trees, there lived a boy. The branches of the burning trees sometimes fell, and the magic in the wood permitted only girls to carry the fallen branches of the burning trees.

One day, a branch fell, and a boy was pinned beneath. The boy saw other boys pinned by branches, rescued by their girl friends, but he remained trapped beneath his own burning branch.

The fire crept closer, and the boy called out for help.

Finally, a friend of his own came, but she told him that she could not free him from the burning branch, because she already free'd her other friend from beneath a burning branch and he would be jealous if she did the same deed for anyone else. This friend left him where he lay, but she did promise to return and visit.

The fire crept closer, and the boy called out for help.

A man stopped, and gave the boy the advice that he'd get out from beneath the burning branch eventually if he just had faith in himself. The boy's reply was that he did have faith in himself, yet he remained trapped beneath the burning branch. The man suggested that perhaps he did not have enough faith, and left with nothing more to offer.

The fire crept closer, and the boy cried out for help.

A girl came along, and said she would free the boy from beneath the burning branch.

But no, her friends said, the boy was a stranger to her, was her heroic virtue worth nothing? Heroic deeds ought to be born from the heart, and made beautiful by love, they insisted. Simply hauling the branch off a boy she did not love would be monstrously crass, and they would not want to be friends with a girl so shamed.

So the girl changed her mind and left with her friends.

The fire crept closer. It began to lick at the boy's skin. A soothing warmth became an uncomfortable heat. The boy mustered his courage and chased the fear out of his own voice. He called out, but not for help. He called out for company.

A girl came along, and the boy asked if she would like to be friends. The girl's reply was that she would like to be friends, but that she spent most of her time on the other side of the village, so if they were to be friends, he must be free from beneath the burning branch.

The boy suggested that she free him from beneath the burning branch, so that they could be friends.

The girl replied that she once free'd a boy from beneath a burning branch who also promised to be her friend, but as soon as he was free he never spoke to her again. So how could she trust the boy's offer of friendship? He would say anything to be free.

The boy tried frantically to convince her that he was sincere, that he would be grateful and try with all his heart to be a good friend to the girl who free'd him, but she did not believe him and turned away from him and left him there to burn.

The fire crept closer and the boy whimpered in pain and fear as it spread from wood to flesh. He cried out for help. He begged for help. "Somebody, please!"

A man and a woman came along, and the man offered advice: he was once trapped beneath a burning branch for several years. The fire was magic, the pain was only an illusion. Perhaps it was sad that he was trapped but even so trapped the boy may lead a fulfilling life. Why, the man remembered etching pictures into his branch, befriending passers by, and making up songs.

The woman beside the man agreed, and told the boy that she hoped the right girl would come along and free him, but that he must not presume that he was entitled to any girl's heroic deed merely because he was trapped beneath a burning branch.

"But do I not deserve to be helped?" the boy pleaded, as the flames licked his skin.

"No, how wrong of you to even speak as though you do. My heroic deeds are mine to give, and to you I owe nothing," he was told.

"Perhaps I don't deserve help from you in particular, or from anyone in particular, but is it not so very cruel of you to say I do not deserve any help at all?" the boy pleaded. "Can a girl willing to free me from beneath this burning branch not be found and sent to my aide?"

"Of course not," he was told, "that is utterly unreasonable and you should be ashamed of yourself for asking. It is offensive that you believe such a girl may even exist. You've become burned and ugly, who would want to save you now?"

The fire spread, and the boy cried, screamed, and begged desperately for help from every passer by.

"It hurts it hurts it hurts oh why will no one free me from beneath this burning branch?!" he wailed in despair. "Anything, anyone, please! I don't care who frees me, I only wish for release from this torment!"

Many tried to ignore him, while others scoffed in disgust that he had so little regard for what a heroic deed ought to be. Some pitied him, and wanted to help, but could not bring themselves to bear the social cost, the loss of worth in their friends' and family's eyes, that would come of doing a heroic deed motivated, not by love, but by something lesser.

The boy burned, and wanted to die.

Another boy stepped forward. He went right up to the branch, and tried to lift it. The trapped boy gasped at the small relief from the burning agony, but it was only a small relief, for the burning branches could only be lifted by girls, and the other boy could not budge it. Though the effort was for naught, the first boy thanked him sincerely for trying.

The boy burned, and wanted to die. He asked to be killed.

He was told he had so much to live for, even if he must live beneath a burning branch. None were willing to end him, but perhaps they could do something else to make it easier for him to live beneath the burning branch? The boy could think of nothing. He was consumed by agony, and wanted only to end.

And then, one day, a party of strangers arrived in the village. Heroes from a village afar. Within an hour, one foreign girl came before the boy trapped beneath the burning branch and told him that she would free him if he gave her his largest nugget of gold.

Of course, the local villagers were shocked that this foreigner would sully a heroic deed by trafficking it for mere gold.

But, the boy was too desperate to be shocked, and agreed immediately. She free'd him from beneath the burning branch, and as the magical fire was drawn from him, he felt his burned flesh become restored and whole. He fell upon the foreign girl and thanked her and thanked her and thanked her, crying and crying tears of relief.

Later, he asked how. He asked why. The foreign girls explained that in their village, heroic virtue was measured by how much joy a hero brought, and not by how much she loved the ones she saved.

The locals did not like the implication that their own way might not have been the best way, and complained to the chief of their village. The chief cared only about staying in the good graces of the heroes of his village, and so he outlawed the trading of heroic deeds for other commodities.

The foreign girls were chased out of the village.

And then a local girl spoke up, and spoke loud, to sway her fellow villagers. The boy recognized her. It was his friend. The one who had promised to visit so long ago.

But she shamed the boy, for doing something so crass as trading gold for a heroic deed. She told him he should have waited for a local girl to free him from beneath the burning branch, or else grown old and died beneath it.

To garner sympathy from her audience, she sorrowfully admitted that she was a bad friend for letting the boy be tempted into something so disgusting. She felt responsible, she claimed, and so she would fix her mistake.

The girl picked up a burning branch. Seeing what she was about to do, the boy begged and pleaded for her to reconsider, but she dropped the burning branch upon the boy, trapping him once more.

The boy screamed and begged for help, but the girl told him that he was morally obligated to learn to live with the agony, and never again voice a complaint, never again ask to be free'd from beneath the burning branch.

"Banish me from the village, send me away into the cold darkness, please! Anything but this again!" the boy pleaded.

"No," he was told by his former friend, "you are better off where you are, where all is proper."

In the last extreme, the boy made a grab for his former friend's leg, hoping to drag her beneath the burning branch and free himself that way, but she evaded him. In retaliation for the attempt to defy her, she had a wall built around the boy, so that none would be able, even if one should want to free him from beneath the burning branch.

With all hope gone, the boy broke and became numb to all possible joys. And thus, he died, unmourned.

Last year, I asked LW for some advice about spaced repetition software (SRS) that might be useful to me as a high school teacher. With said advice came a request to write a follow-up after I had accumulated some experience using SRS in the classroom. This is my report.

Please note that this was not a scientific experiment to determine whether SRS "works." Prior studies are already pretty convincing on this point and I couldn't think of a practical way to run a control group or "blind" myself. What follows is more of an informal debriefing for how I used SRS during the 2014-15 school year, my insights for others who might want to try it, and how the experience is changing how I teach.

Summary

SRS can raise student achievement even with students who won't use the software on their own, and even with frequent disruptions to the study schedule. Gains are most apparent with the already high-performing students, but are also meaningful for the lowest students. Deliberate efforts are needed to get student buy-in, and getting the most out of SRS may require changes in course design.

The software

After looking into various programs, including the game-like Memrise, and even writing my own simple SRS, I ultimately went with Anki for its multi-platform availability, cloud sync, and ease-of-use. I also wanted a program that could act as an impromptu catch-all bin for the 2,000+ cards I would be producing on the fly throughout the year. (Memrise, in contrast, really needs clearly defined units packaged in advance).

The students

I teach 9th and 10th grade English at an above-average suburban American public high school in a below-average state. Mine are the lower "required level" students at a school with high enrollment in honors and Advanced Placement classes. Generally speaking, this means my students are mostly not self-motivated, are only very weakly motivated by grades, and will not do anything school-related outside of class no matter how much it would be in their interest to do so. There are, of course, plenty of exceptions, and my students span an extremely wide range of ability and apathy levels.

The procedure

First, what I did not do. I did not make Anki decks, assign them to my students to study independently, and then quiz them on the content. With honors classes I taught in previous years I think that might have worked, but I know my current students too well. Only about 10% of them would have done it, and the rest would have blamed me for their failing grades—with some justification, in my opinion.

Instead, we did Anki together, as a class, nearly every day.

As initial setup, I created a separate Anki profile for each class period. With a third-party add-on for Anki called Zoom, I enlarged the display font sizes to be clearly legible on the interactive whiteboard at the front of my room.

Nightly, I wrote up cards to reinforce new material and integrated them into the deck in time for the next day's classes. This averaged about 7 new cards per lesson period.These cards came in many varieties, but the three main types were:

1. concepts and terms, often with reversed companion cards, sometimes supplemented with "what is this an example of" scenario cards.
2. vocabulary, 3 cards per word: word/def, reverse, and fill-in-the-blank example sentence
3. grammar, usually in the form of "What change(s), if any, does this sentence need?" Alternative cards had different permutations of the sentence.

Weekly, I updated the deck to the cloud for self-motivated students wishing to study on their own.

Daily, I led each class in an Anki review of new and due cards for an average of 8 minutes per study day, usually as our first activity, at a rate of about 3.5 cards per minute. As each card appeared on the interactive whiteboard, I would read it out loud while students willing to share the answer raised their hands. Depending on the card, I might offer additional time to think before calling on someone to answer. Depending on their answer, and my impressions of the class as a whole, I might elaborate or offer some reminders, mnemonics, etc. I would then quickly poll the class on how they felt about the card by having them show a color by way of a small piece of card-stock divided into green, red, yellow, and white quadrants. Based on my own judgment (informed only partly by the poll), I would choose and press a response button in Anki, determining when we should see that card again.

[Data shown is from one of my five classes. We didn't start using Anki until a couple weeks into the school year.]

Opportunity costs

8 minutes is a significant portion of a 55 minute class period, especially for a teacher like me who fills every one of those minutes. Something had to give. For me, I entirely cut some varieties of written vocab reinforcement, and reduced the time we spent playing the team-based vocab/term review game I wrote for our interactive whiteboards some years ago. To a lesser extent, I also cut back on some oral reading comprehension spot-checks that accompany my whole-class reading sessions. On balance, I think Anki was a much better way to spend the time, but it's complicated. Keep reading.

Whole-class SRS not ideal

Every student is different, and would get the most out of having a personal Anki profile determine when they should see each card. Also, most individuals could study many more cards per minute on their own than we averaged doing it together. (To be fair, a small handful of my students did use the software independently, judging from Ankiweb download stats)

Getting student buy-in

Before we started using SRS I tried to sell my students on it with a heartfelt, over-prepared 20 minute presentation on how it works and the superpowers to be gained from it. It might have been a waste of time. It might have changed someone's life. Hard to say.

As for the daily class review, I induced engagement partly through participation points that were part of the final semester grade, and which students knew I tracked closely. Raising a hand could earn a kind of bonus currency, but was never required—unlike looking up front and showing colors during polls, which I insisted on. When I thought students were just reflexively holding up the same color and zoning out, I would sometimes spot check them on the last card we did and penalize them if warranted.

But because I know my students are not strongly motivated by grades, I think the most important influence was my attitude. I made it a point to really turn up the charm during review and play the part of the engaging game show host. Positive feedback. Coaxing out the lurkers. Keeping that energy up. Being ready to kill and joke about bad cards. Reminding classes how awesome they did on tests and assignments because they knew their Anki stuff.

(This is a good time to point out that the average review time per class period stabilized at about 8 minutes because I tried to end reviews before student engagement tapered off too much, which typically started happening at around the 6-7 minute mark. Occasional short end-of-class reviews mostly account for the difference.)

I also got my students more on the Anki bandwagon by showing them how this was directly linked reduced note-taking requirements. If I could trust that they would remember something through Anki alone, why waste time waiting for them to write it down? They were unlikely to study from those notes anyway. And if they aren't looking down at their paper, they'll be paying more attention to me. I better come up with more cool things to tell them!

Making memories

Everything I had read about spaced repetition suggested it was a great reinforcement tool but not a good way to introduce new material. With that in mind, I tried hard to find or create memorable images, examples, mnemonics, and anecdotes that my Anki cards could become hooks for, and to get those cards into circulation as soon as possible. I even gave this method a mantra: "vivid memory, card ready".

When a student during review raised their hand, gave me a pained look, and said, "like that time when...." or "I can see that picture of..." as they struggled to remember, I knew I had done well. (And I would always wait a moment, because they would usually get it.)

Baby cards need immediate love

Unfortunately, if the card wasn't introduced quickly enough—within a day or two of the lesson—the entire memory often vanished and had to be recreated, killing the momentum of our review. This happened far too often—not because I didn't write the card soon enough (I stayed really on top of that), but because it didn't always come up for study soon enough. There were a few reasons for this:

1. We often had too many due cards to get through in one session, and by default Anki puts new cards behind due ones.
2. By default, Anki only introduces 20 new cards in one session (I soon uncapped this).
3. Some cards were in categories that I gave lower priority to.

Two obvious cures for this problem:

1. Make fewer cards. (I did get more selective as the year went on.)
2. Have all cards prepped ahead of time and introduce new ones at the end of the class period they go with. (For practical reasons, not the least of which was the fact that I didn't always know what cards I was making until after the lesson, I did not do this. I might able to next year.)

Days off suck

SRS is meant to be used every day. When you take weekends off, you get a backlog of due cards. Not only do my students take every weekend and major holiday off (slackers), they have a few 1-2 week vacations built into the calendar. Coming back from a week's vacation means a 9-day backlog (due to the weekends bookending it). There's no good workaround for students that won't study on their own. The best I could do was run longer or multiple Anki sessions on return days to try catch up with the backlog. It wasn't enough. The "caught up" condition was not normal for most classes at most points during the year, but rather something to aspire to and occasionally applaud ourselves for reaching. Some cards spent weeks or months on the bottom of the stack. Memories died. Baby cards emerged stillborn. Learning was lost.

Needless to say, the last weeks of the school year also had a certain silliness to them. When the class will never see the card again, it doesn't matter whether I push the button that says 11 days or the one that says 8 months. (So I reduced polling and accelerated our cards/minute rate.)

Never before SRS did I fully appreciate the loss of learning that must happen every summer break.

Triage

I kept each course's master deck divided into a few large subdecks. This was initially for organizational reasons, but I eventually started using it as a prioritizing tool. This happened after a curse-worthy discovery: if you tell Anki to review a deck made from subdecks, due cards from subdecks higher up in the stack are shown before cards from decks listed below, no matter how overdue they might be. From that point, on days when we were backlogged (most days) I would specifically review the concept/terminology subdeck for the current semester before any other subdecks, as these were my highest priority.

On a couple of occasions, I also used Anki's study deck tools to create temporary decks of especially high-priority cards.

Seizing those moments

Veteran teachers start acquiring a sense of when it might be a good time to go off book and teach something that isn't in the unit, and maybe not even in the curriculum. Maybe it's teaching exactly the right word to describe a vivid situation you're reading about, or maybe it's advice on what to do in a certain type of emergency that nearly happened. As the year progressed, I found myself humoring my instincts more often because of a new confidence that I can turn an impressionable moment into a strong memory and lock it down with a new Anki card. I don't even care if it will ever be on a test. This insight has me questioning a great deal of what I thought knew about organizing a curriculum. And I like it.

A lifeline for low performers

An accidental discovery came from having written some cards that were, it was immediately obvious to me, much too easy. I was embarrassed to even be reading them out loud. Then I saw which hands were coming up.

In any class you'll get some small number of extremely low performers who never seem to be doing anything that we're doing, and, when confronted, deny that they have any ability whatsoever. Some of the hands I was seeing were attached to these students. And you better believe I called on them.

It turns out that easy cards are really important because they can give wins to students who desperately need them. Knowing a 6th grade level card in a 10th grade class is no great achievement, of course, but the action takes what had been negative morale and nudges it upward. And it can trend. I can build on it. A few of these students started making Anki the thing they did in class, even if they ignored everything else. I can confidently name one student I'm sure passed my class only because of Anki. Don't get me wrong—he just barely passed. Most cards remained over his head. Anki was no miracle cure here, but it gave him and I something to work with that we didn't have when he failed my class the year before.

A springboard for high achievers

It's not even fair. The lowest students got something important out of Anki, but the highest achievers drank it up and used it for rocket fuel. When people ask who's widening the achievement gap, I guess I get to raise my hand now.

I refuse to feel bad for this. Smart kids are badly underserved in American public schools thanks to policies that encourage staff to focus on that slice of students near (but not at) the bottom—the ones who might just barely be able to pass the state test, given enough attention.

Where my bright students might have been used to high Bs and low As on tests, they were now breaking my scales. You could see it in the multiple choice, but it was most obvious in their writing: they were skillfully working in terminology at an unprecedented rate, and making way more attempts to use new vocabulary—attempts that were, for the most part, successful.

Given the seemingly objective nature of Anki it might seem counterintuitive that the benefits would be more obvious in writing than in multiple choice, but it actually makes sense when I consider that even without SRS these students probably would have known the terms and the vocab well enough to get multiple choice questions right, but might have lacked the confidence to use them on their own initiative. Anki gave them that extra confidence.

A wash for the apathetic middle?

I'm confident that about a third of my students got very little out of our Anki review. They were either really good at faking involvement while they zoned out, or didn't even try to pretend and just took the hit to their participation grade day after day, no matter what I did or who I contacted.

These weren't even necessarily failing students—just the apathetic middle that's smart enough to remember some fraction of what they hear and regurgitate some fraction of that at the appropriate times. Review of any kind holds no interest for them. It's a rerun. They don't really know the material, but they tell themselves that they do, and they don't care if they're wrong.

On the one hand, these students are no worse off with Anki than they would have been with with the activities it replaced, and nobody cries when average kids get average grades. On the other hand, I'm not ok with this... but so far I don't like any of my ideas for what to do about it.

Putting up numbers: a case study

For unplanned reasons, I taught a unit at the start of a quarter that I didn't formally test them on until the end of said quarter. Historically, this would have been a disaster. In this case, it worked out well. For five weeks, Anki was the only ongoing exposure they were getting to that unit, but it proved to be enough. Because I had given the same test as a pre-test early in the unit, I have some numbers to back it up. The test was all multiple choice, with two sections: the first was on general terminology and concepts related to the unit. The second was a much harder reading comprehension section.

As expected, scores did not go up much on the reading comprehension section. Overall reading levels are very difficult to boost in the short term and I would not expect any one unit or quarter to make a significant difference. The average score there rose by 4 percentage points, from 48 to 52%.

Scores in the terminology and concept section were more encouraging. For material we had not covered until after the pre-test, the average score rose by 22 percentage points, from 53 to 75%. No surprise there either, though; it's hard to say how much credit we should give to SRS for that.

But there were also a number of questions about material we had already covered before the pretest. Being the earliest material, I might have expected some degradation in performance on the second test. Instead, the already strong average score in that section rose by an additional 3 percentage points, from 82 to 85%. (These numbers are less reliable because of the smaller number of questions, but they tell me Anki at least "locked in" the older knowledge, and may have strengthened it.)

Some other time, I might try reserving a section of content that I teach before the pre-test but don't make any Anki cards for. This would give me a way to compare Anki to an alternative review exercise.

What about formal standardized tests?

I don't know yet. The scores aren't back. I'll probably be shown some "value added" analysis numbers at some point that tell me whether my students beat expectations, but I don't know how much that will tell me. My students were consistently beating expectations before Anki, and the state gave an entirely different test this year because of legislative changes. I'll go back and revise this paragraph if I learn anything useful.

Those discussions...

If I'm trying to acquire a new skill, one of the first things I try to do is listen to skilled practitioners of that skill talk about it to each other. What are the terms-of-art? How do they use them? What does this tell me about how they see their craft? Their shorthand is a treasure trove of crystallized concepts; once I can use it the same way they do, I find I'm working at a level of abstraction much closer to theirs.

Similarly, I was hoping Anki could help make my students more fluent in the subject-specific lexicon that helps you score well in analytical essays. After introducing a new term and making the Anki card for it, I made extra efforts to use it conversationally. I used to shy away from that because so many students would have forgotten it immediately and tuned me out for not making any sense. Not this year. Once we'd seen the card, I used the term freely, with only the occasional reminder of what it meant. I started using multiple terms in the same sentence. I started talking about writing and analysis the way my fellow experts do, and so invited them into that world.

Even though I was already seeing written evidence that some of my high performers had assimilated the lexicon, the high quality discussions of these same students caught me off guard. You see, I usually dread whole-class discussions with non-honors classes because good comments are so rare that I end up dejectedly spouting all the insights I had hoped they could find. But by the end of the year, my students had stepped up.

I think what happened here was, as with the writing, as much a boost in confidence as a boost in fluency. Whatever it was, they got into some good discussions where they used the terminology and built on it to say smarter stuff.

Don't get me wrong. Most of my students never got to that point. But on average even small groups without smart kids had a noticeably higher level of discourse than I am used to hearing when I break up the class for smaller discussions.

Limitations

SRS is inherently weak when it comes to the abstract and complex. No card I've devised enables a student to develop a distinctive authorial voice, or write essay openings that reveal just enough to make the reader curious. Yes, you can make cards about strategies for this sort of thing, but these were consistently my worst cards—the overly difficult "leeches" that I eventually suspended from my decks.

A less obvious limitation of SRS is that students with a very strong grasp of a concept often fail to apply that knowledge in more authentic situations. For instance, they may know perfectly well the difference between "there", "their", and "they're", but never pause to think carefully about whether they're using the right one in a sentence. I am very open to suggestions about how I might train my students' autonomous "System 1" brains to have "interrupts" for that sort of thing... or even just a reflex to go back and check after finishing a draft.

Moving forward

I absolutely intend to continue using SRS in the classroom. Here's what I intend to do differently this coming school year:

• Reduce the number of cards by about 20%, to maybe 850-950 for the year in a given course, mostly by reducing the number of variations on some overexposed concepts.
• Be more willing to add extra Anki study sessions to stay better caught-up with the deck, even if this means my lesson content doesn't line up with class periods as neatly.
• Be more willing to press the red button on cards we need to re-learn. I think I was too hesitant here because we were rarely caught up as it was.
• Rework underperforming cards to be simpler and more fun.
• Use more simple cloze deletion cards. I only had a few of these, but they worked better than I expected for structured idea sets like, "characteristics of a tragic hero".
• Take a less linear and more opportunistic approach to introducing terms and concepts.
• Allow for more impromptu discussions where we bring up older concepts in relevant situations and build on them.
• Shape more of my lessons around the "vivid memory, card ready" philosophy.
• Continue to reduce needless student note-taking.
• Keep a close eye on 10th grade students who had me for 9th grade last year. I wonder how much they retained over the summer, and I can't wait to see what a second year of SRS will do for them.

Suggestions and comments very welcome!

LW has often discussed the inductive logic game Zendo, as a possible way of training rationality. But I couldn't find any computer implementations of Zendo online.

So I built two (fairly similar) games inspired by Zendo; they generate rules and play as sensei. The code is on GitHub, along with some more explanation. To run the games you'll need to install Python 3, and Scikit-Learn for the second game; see the readme.

All bugfixes and improvements are welcome. For instance, more rule classes or features would improve the game and be pretty easy to code. Also, if anyone has a website and wants to host this playable online (with CGI, say), that would be awesome.

Savory

What does "savory" mean when talking about food? Merriam-Webster says:

• having a pleasant taste or smell
• having a spicy or salty quality without being sweet
• pleasing to the sense of taste especially by reason of effective seasoning
• pungently flavorful without sweetness

Macmillan says:

• a small piece of food that tastes of salt or spices and is not sweet

But when found in the wild, "savory" is usually contrasted with sweet, and is either freed from the "salt or spices" requirement, or used in a context that already implies "salty, spicy, or sweet." As this debate on chowhounds shows, plenty of cooks think "savory" means "not sweet." It is then not a category, but an uncategory, defined by what it is not.

There's widespread confusion about the nature of mathematical ability, for a variety of reasons:

• Most people don't know what math is.
• Most people don't know enough statistics to analyze the question properly.
• Most mathematicians are not very metacognitive.
• Very few people have more than a casual interest in the subject.

If the nature of mathematical ability were exclusively an object of intellectual interest, this would be relatively inconsequential. For example, many people are confused about Einstein’s theory of relativity, but this doesn’t have much of an impact on their lives. But in practice, people’s misconceptions about the nature of mathematical ability seriously interfere with their own ability to learn and do math, something that hurts them both professionally and emotionally.

I have a long standing interest in the subject, and I’ve found myself in the unusual position of being an expert. My experiences include:

• Completing a PhD in pure math at University of Illinois.
• Four years of teaching math at the high school and college levels (precalculus, calculus, multivariable calculus and linear algebra)
• Personal encounters with some of the best mathematicians in the world, and a study of great mathematicians’ biographies.
• A long history of working with mathematically gifted children: as a counselor at MathPath for three summers, through one-on-one tutoring, and as an instructor at Art of Problem Solving.
• Studying the literature on IQ and papers from the Study of Exceptional Talent as a part of my work for Cognito Mentoring.
• Training as a full-stack web developer at App Academy.
• Doing a large scale data science project where I applied statistics and machine learning to make new discoveries in social psychology.

I’ve thought about writing about the nature of mathematical ability for a long time, but there was a missing element: I myself had never done genuinely original and high quality mathematical research. After completing much of my data science project, I realized that this had changed. The experience sharpened my understanding of the issues.

This is a the first of a sequence of posts where I try to clarify the situation. My main point in this post is:

There are several different dimensions to mathematical ability. Common measures rarely assess all of these dimensions, and can paint a very incomplete picture of what somebody is capable of.

From Scott Adams Blog

The article really is about speeding up government, but the key point is speed as a component of smart: 

A smart friend told me recently that speed is the new intelligence, at least for some types of technology jobs. If you are hiring an interface designer, for example, the one that can generate and test several designs gets you further than the “genius” who takes months to produce the first design to test. When you can easily test alternatives, the ability to quickly generate new things to test is a substitute for intelligence.

This shifts the focus from the ability to grasp and think through very complex topics (includes good working memory and memory recall in general) to the ability new topics quickly (includes quick learning and unlearning, creativity).

Smart people in the technology world no long believe they can think their way to success. Now the smart folks try whatever plan looks promising, test it, tweak it, and reiterate. In that environment, speed matters more than intelligence because no one has the psychic ability to pick a winner in advance. All you can do is try things that make sense and see what happens. Obviously this is easier to do when your product is software based.

This also changes the type of grit needed. The grit to push through a long topic versus the grit try lots of new things and to learn from failures.

A lottery ticket sometimes has positive expected value, (a $1 ticket might be expected to pay out $1.30). How many tickets should you buy?

Probably none. Informally, all but the richest players can expect to go broke before they win, despite the positive expected value of a ticket.

In more precise terms: In order to maximize the long-term growth rate of your money (or log money), you'll want to put a very small fraction of your bankroll into lotteries tickets, which will imply an "amount to invest" that is less than the cost of a single ticket, (excluding billionaires). If you put too great a proportion of your resources into a risky but positive expected value asset, the long-term growth rate of your resources can become negative. For an intuitive example, imagine Bill Gates dumping 99% percent of his wealth into a series of positive expected-value bets with single-lottery-ticket-like odds.

This article has some graphs and details on the lottery. This pdf on the Kelly criterion has some examples and general dicussion of this type of problem.

Can we think about Pascal mugging the same way?

The applicability might depend on whether we're trading resource-generating-resources for non-resource-generating assets. So if we're offered something like cash, the lottery ticket model (with payout inversely varying with estimated odds) is a decent fit. But what if we're offered utility in some direct and non-interest-bearing form?

Another limit: For a sufficiency unlikely but positive-expected-value gamble, you can expect the heat death of the universe before actually realizing any of the expected value.

Has no one else mentioned this on LW yet?

Elizabeth Edwards has been elected as a New Hampshire State Rep, self-identifies as a Rationalist and explicitly mentions Less Wrong in her first post-election blog post.

Sorry if this is a repost

I have taken this well received post by Eliezer, and remade the first third of it into a short and quickly paced youtube video here: http://youtu.be/L2dNANRIALs

The goals of this post are re-introducing the lessons explored in the original (for anyone not yet familiar with them), as well as asking the question of whether this format is actually suited for the lessons LessWrong tries to teach. What are your thoughts?

I think it'd be a good idea to keep a list of the ways we'd like to see LessWrong improve, sorted by popularity. Ie. email alerts for new responses.

So if you have an idea for how LessWrong could be better, post it in the comments. As people up/downvote, we'll get a sense for what the consensus opinions are.

I think there's a pretty good amount to be gained by improving LessWrong.

• I think there's a lot of low-hanging fruit (like email alerts for new responses).
• Conversations here are actually useful and productive. Facilitating conversation should thus lead to more of these useful and productive conversations (as opposed to leading to more of an unproductive type of conversation). (Sorry, I didn't word this well; hopefully you guys know what I mean.)
• Perhaps something big would come out of this list (like meet-ups). Perhaps rationality hack-a-thons (whatever that means)? 

Note: I say "ways to improve" instead of "features" because "ways to improve" is more general.