The Best Textbooks on Every Subject
For years, my self-education was stupid and wasteful. I learned by consuming blog posts, Wikipedia articles, classic texts, podcast episodes, popular books, video lectures, peer-reviewed papers, Teaching Company courses, and Cliff's Notes. How inefficient!
I've since discovered that textbooks are usually the quickest and best way to learn new material. That's what they are designed to be, after all. Less Wrong has often recommended the "read textbooks!" method. Make progress by accumulation, not random walks.
But textbooks vary widely in quality. I was forced to read some awful textbooks in college. The ones on American history and sociology were memorably bad, in my case. Other textbooks are exciting, accurate, fair, well-paced, and immediately useful.
What if we could compile a list of the best textbooks on every subject? That would be extremely useful.
Let's do it.
There have been other pages of recommended reading on Less Wrong before (and elsewhere), but this post is unique. Here are the rules:
- Post the title of your favorite textbook on a given subject.
- You must have read at least two other textbooks on that same subject.
- You must briefly name the other books you've read on the subject and explain why you think your chosen textbook is superior to them.
Rules #2 and #3 are to protect against recommending a bad book that only seems impressive because it's the only book you've read on the subject. Once, a popular author on Less Wrong recommended Bertrand Russell's A History of Western Philosophy to me, but when I noted that it was more polemical and inaccurate than the other major histories of philosophy, he admitted he hadn't really done much other reading in the field, and only liked the book because it was exciting.
I'll start the list with three of my own recommendations...
The new GiveWell recommendations are out: here's a summary of the charities
GiveWell have just announced their latest charity recommendations! What are everyone’s thoughts on them?
A summary: all of the old charities (GiveDirectly, SCI and Deworm the World) remain on the list. They're rejoined by AMF, as the room for more funding issues that led to it being delisted have been resolved to GiveWell's satisfaction. Together these organisations form GiveWell's list of 'top charities', which is now joined by a list of other charities which they see as excellent but not quite in the top tier. The charities on this list are Development Media International, Living Goods, and two salt fortification programs (run by GAIN and ICCIDD).
As normal, GiveWell's site contains extremely detailed writeups on these organisations. Here are some shorter descriptions which I wrote for Charity Science's donations page and my tool for donating tax-efficiently, starting with the new entries:
GiveWell's newly-added charities
Boost health and cognitive development with salt fortification
The charities GAIN and ICCIDD run programs that fortify the salt that millions of poor people eat with iodine. There is strong evidence that this boosts their health and cognitive development; iodine deficiency causes pervasive mental impairment, as well as stillbirth and congenital abnormalities such as severe retardation. It can be done very cheaply on a mass scale, so is highly cost-effective. GAIN is registered in the US and ICCIDD in Canada (although Canadians can give to either via Charity Science, which for complex reasons helps others who donate tax-deductibly to other charities), allowing for especially efficient donations from these countries, and taxpayers from other countries can also often give to them tax-deductibly. For more information, read GiveWell's detailed reviews of GAIN and ICCIDD.
Educate millions in life-saving practices with Development Media International
Development Media International (DMI) produces radio and television broadcasts in developing countries that tell people about improved health practices that can save lives, especially those of young children. Examples of such practices include exclusive breastfeeding. DMI are conducting a randomized controlled trial of their program which has found promising indications of a large decrease in children's deaths. With more funds they would be able to reach millions of people, due to the unparalleled reach of broadcasting. For more information, read GiveWell's detailed review.
Bring badly-needed goods and health services to the poor with Living Goods
Living Goods is a non-profit which runs a network of people selling badly-needed health and household goods door-to-door in their communities in Uganda and Kenya and provide free health advice. A randomized controlled trial suggested that this caused a 25% reduction in under-5 mortality among other benefits. Products sold range from fortified foods and mosquito nets to cookstoves and contraceptives. Giving to Living Goods is an exciting opportunity to bring these badly needed goods and services to some of the poorest families in the world. For more information, read GiveWell's detailed review.
GiveWell's old and returning charities
Treat hundreds of people for parasitic worms
Deworm the World and the Schistosomiasis Control Initiative (SCI) treat parasitic worm infections such as schistosomiasis, which can cause urinary infections, anemia, and other nutritional problems. For more information, read GiveWell's detailed review, or the more accessible Charity Science summary. Deworm the World is registered in the USA and SCI in the UK, allowing for tax-efficient direct donations in those countries, and taxpayers from other countries can also often give to them efficiently.
Make unconditional cash transfers with GiveDirectly
GiveDirectly lets you empower people to purchase whatever they believe will help them most. Eleven randomized controlled trials have supported cash transfers’ impact, and there is strong evidence that recipients know their own situation best and generally invest in things which make them happier in the long term. For more information, read GiveWell's detailed review, or the more accessible Charity Science summary.
Save lives and prevent infections with the Against Malaria Foundation
Malaria causes about a million deaths and two hundred million infections a year. Thankfully a $6 bednet can stop mosquitos from infecting children while they sleep, preventing this deadly disease. This intervention has exceptionally robust evidence behind it, with many randomized controlled trials suggesting that it is one of the most cost-effective ways to save lives. The Against Malaria Foundation (AMF) is an exceptional charity in every respect, and was GiveWell's top recommendation in 2012 and 2013. Not all bednet charities are created equal, and AMF outperforms the rest on every count. They can distribute nets cheaper than most others, for just $6.13 US. They distribute long-lasting nets which don’t need retreating with insecticide. They are extremely transparent and monitor their own impact carefully, requiring photo verification from each net distribution. For more information, read GiveWell's detailed review, or the more accessible Charity Science summary.
How to donate
To find out which charities are tax-deductible in your country and get links to give to them tax-efficiently, you can use this interactive tool that I made. If you give this season, consider sharing the charities you choose on the EA Donation Registry. We can see which charities EAs pick, and which of the new ones prove popular!
Systemic risk: a moral tale of ten insurance companies
Once upon a time...
Imagine there were ten insurance sectors, each sector being a different large risk (or possibly the same risks, in different geographical areas). All of these risks are taken to be independent.
To simplify, we assume that all the risks follow the same yearly payout distributions. The details of the distribution doesn't matter much for the argument, but in this toy model, the payouts follow the discrete binomial distribution with n=10 and p=0.5, with millions of pounds as the unit:

This means that the probability that each sector pays out £n million each year is (0.5)10 . 10!/(n!(10-n)!).
All these companies are bound by Solvency II-like requirements, that mandate that they have to be 99.5% sure to payout all their policies in a given year - or, put another way, that they only fail to payout once in every 200 years on average. To do so, in each sector, the insurance companies have to have capital totalling £9 million available every year (the red dashed line).
Assume that each sector expects £1 million in total yearly expected profit. Then since the expected payout is £5 million, each sector will charge £6 million a year in premiums. They must thus maintain a capital reserve of £3 million each year (they get £6 million in premiums, and must maintain a total of £9 million). They thus invest £3 million to get an expected profit of £1 million - a tidy profit!
Every two hundred years, one of the insurance sectors goes bust and has to be bailed out somehow; every hundred billion trillion years, all ten insurance sectors go bust all at the same time. We assume this is too big to be bailed out, and there's a grand collapse of the whole insurance industry with knock on effects throughout the economy.
But now assume that insurance companies are allowed to invest in each other's sectors. The most efficient way of doing so is to buy equally in each of the ten sectors. The payouts across the market as a whole are now described by the discrete binomial distribution with n=100 and p=0.5:

This is a much narrower distribution (relative to its mean). In order to have enough capital to payout 99.5% of the time, the whole industry needs only keep £63 million in capital (the red dashed line). Note that this is far less that the combined capital for each sector when they were separate, which would be ten times £9 million, or £90 million (the pink dashed line). There is thus a profit taking opportunity in this area (it comes from the fact that the standard deviation of X+Y is less that the standard deviation of X plus the standard deviation Y).
If the industry still expects to make an expected profit of £1 million per sector, this comes to £10 million total. The expected payout is £50 million, so they will charge £60 million in premium. To accomplish their Solvency II obligations, they still need to hold an extra £3 million in capital (since £63 million - £60 million = £3 million). However, this is now across the whole insurance industry, not just per sector.
Thus they expect profits of £10 million based on holding capital of £3 million - astronomical profits! Of course, that assumes that the insurance companies capture all the surplus from cross investing; in reality there would be competition, and a buyer surplus as well. But the general point is that there is a vast profit opportunity available from cross-investing, and thus if these investments are possible, they will be made. This conclusion is not dependent on the specific assumptions of the model, but captures the general result that insuring independent risks reduces total risk.
But note what has happened now: once every 200 years, an insurance company that has spread their investments across the ten sectors will be unable to payout what they owe. However, every company will be following this strategy! So when one goes bust, they all go bust. Thus the complete collapse of the insurance industry is no longer a one in hundred billion trillion year event, but a one in two hundred year event. The risk for each company has stayed the same (and their profits have gone up), but the systemic risk across the whole insurance industry has gone up tremendously.
...and they failed to live happily ever after for very much longer.
Creating The Simple Math of Everything
Eliezer once proposed an Idea for a book, The Simple Math of Everything. The basic idea is to compile articles on the basic mathematics of a wide variety of fields, but nothing too complicated.
Not Jacobean matrices for frequency-dependent gene selection; just Haldane's calculation of time to fixation. Not quantum physics; just the wave equation for sound in air. Not the maximum entropy solution using Lagrange Multipliers; just Bayes's Rule.
Now, writing a book is a pretty daunting task. Luckily brian_jaress had the idea of creating an index of links to already available online articles. XFrequentist pointed out that something like this has been done before over at Evolving Thoughts. This initially discourage me, but it eventually helped me refine what I thought the index should be. A key characteristic of Eliezer's idea is that it should be worthwhile for someone who doesn't know the material to read the entire index. Many of the links at evolving thoughts point to rather narrow topics that might not be very interesting to a generalist. Also there is just plain a ton of stuff to read over there - at least 100 articles.
So we should come up with some basic criteria for the articles. Here is what I suggest (let me know what you think):
The Atheist's Tithe
I made a comment on another site a week or two ago, and I just realized that the line of thought is one that LW would appreciate, so here's a somewhat expanded version.
There's a lot of discussion around here about how to best give to charities, and I'm all for this. Ensuring donations are used well is important, and organizations like GiveWell that figure out how to get the most bang for your buck are doing very good work. An old article on LW (that I found while searching to make sure I wasn't being redundant by posting this) makes the claim that the difference between a decent charity and an optimal one can be two orders of magnitude, and I believe that. But the problem with this is, effective altruism only helps if people are actually giving money.
People today don't tend to give very much to charity. They'll buy a chocolate bar for the school play or throw a few bucks in at work, but less than 2% of national income is donated even in the US, and the US is incredibly charitable by developed-world standards(the corresponding rate in Germany is about 0.1%, for example). And this isn't something that can be solved with math, because the general public doesn't speak math, it needs to be solved with social pressure.
The social pressure needs to be chosen well. Folks like Jeff Kaufman and Julia Wise giving a massive chunk of their income to charity are of course laudable, but 99%+ of people will regard the thought of doing so with disbelief and a bit of horror - it's simply not going to happen on a large scale, because people put themselves first, and don't think they could possibly part with so much of their income. We need to settle for a goal that is not only attainable by the majority of people, but that the majority of people know in their guts is something they could do if they wanted. Not everyone will follow through, but it should be set at a level that inspires guilt if they don't, not laughter.
Since we're trying to make it something people can live up to, it has to be proportional giving, not absolute - Bill Gates and Warren Buffett telling each other to donate everything over a billion is wonderful, but doesn't affect many other people. Conversely, telling people that everything over $50k should be donated will get the laugh reaction from ordinary-wealthy folks like doctors and accountants, who are the people we most want to tie into this system. Also, even if it was workable, it creates some terrible disincentives to working extra-hard, which is a bad way to structure a system - we want to maximize donations, not merely ask people to suffer for its own sake.
Also, the rule needs to be memorable - we can't give out The Income Tax Act 2: Electric Boogaloo as our charitable donation manual, because people won't read it, won't remember it, and certainly won't pressure anyone else into following it. Ideally it should be extremely simple. And it'd be an added bonus if the amount chosen didn't seem arbitrary, if there was already a pre-existing belief that the number is generally appropriate for what part of your income should be given away.
There's only one system that meets all these criteria - the tithe. Give away 10% of your income to worthy causes(not generally religion, though the religious folk of the world can certainly do so), keep 90% for yourself. It's practical, it's simple, it's guilt-able, it scales to income, it preserves incentives to work hard and thereby increase the total base of donations, and it's got a millennia-long tradition(which means both that it's proven to work and that people will believe it's a reasonable thing to expect).
Encouraging people to give more than that, or to give better than the default, are both worthwhile, but just like saving for retirement, the first thing to do is put enough money in, and only *then* worry about marginal changes in effectiveness. After all, putting Germany on the tithe rule is just as much of an improvement to charitable effectiveness as going from a decent charity to an excellent one, and it scales in a completely different way, so they can be worked on in parallel.
This is a rule that I try to follow myself, and sometimes encourage others to do while I'm wearing my financial-advisor hat. (And speaking with that hat: If you're a person who will actually follow through on this, avoid chipping in a few dollars here and there when people ask, and save up for bigger donations. That way you get tax receipts, which lower your effective cost of donation, as well as letting you pick better charities).
The "best" mathematically-informed topics?
Recently, I asked LessWrong about the important math of rationality. I found the responses extremely helpful, but thinking about it, I think there’s a better approach.
I come from a new-age-y background. As such, I hear a lot about “quantum physics.”

Accordingly, I have developed a heuristic that I have found broadly useful: If a field involves math, and you cannot do the math, you are not qualified to comment on that field. If you can’t calculate the Schrödinger equation, I discount whatever you may say about what quantum physics reveals about reality.
Instead of asking which field of math are “necessary” (or useful) to “rationality,” I think it’s more productive to ask, “what key questions or ideas, involving math, would I like to understand?” Instead of going out of my way to learn the math that I predict will be useful, I’ll just embark on trying understand the problems that I’m learning the math for, and working backwards to figure out what math I need for any particular problem. This has the advantage of never causing me to waste time on extraneous topics: I’ll come to understand the concepts I’ll need most frequently best, because I’ll encounter them most frequently (for instance, I think I’ll quickly realize that I need to get a solid understanding of calculus, and so study calculus, but there may be parts of math that don't crop up much, so I'll effectively skip those). While I usually appreciate the aesthetic beauty of abstract math, I think this sort of approach will also help keep me focused and motivated. Note, that at this point, I’m trying to fill in the gaps in my understanding and attain “mathematical literacy” instead of a complete and comprehensive mathematical understanding (a worthy goal that I would like to pursue, but which is of lesser priority to me).
I think even a cursory familiarity with these subjects is likely to be very useful: when someone mentions say, an economic concept, I suspect that the value of even just vaguely remembering having solved a basic version of the problem will give me a significant insight into what the person is talking about, instead of having a hand-wavy, non-mathematical conception.
Eliezer said in the simple math of everything:
It seems to me that there's a substantial advantage in knowing the drop-dead basic fundamental embarrassingly simple mathematics in as many different subjects as you can manage. Not, necessarily, the high-falutin' complicated damn math that appears in the latest journal articles. Not unless you plan to become a professional in the field. But for people who can read calculus, and sometimes just plain algebra, the drop-dead basic mathematics of a field may not take that long to learn. And it's likely to change your outlook on life more than the math-free popularizations or the highly technical math.
(Does anyone with more experience than me foresee problems with this approach? Has this been tired before? How did it work?)
So, I’m asking you: what are some mathematically-founded concepts that are worth learning? Feel free to suggest things for their practical utility or their philosophical insight. Keep in mind that there is a relevant cost benefit analysis to consider: there are some concepts that are really cool to understand, but require many levels of math to get to. (I think after people have responded here, I’ll put out another post for people to vote on a good order to study these things, starting with those topics that have the minimal required mathematical foundation and working up to the complex higher level topics that require calculus, linear algebra, matrices, and analysis.)
These are some things that interest me:
- The math of natural selection and evolution
- The Schrödinger equation
- The math of governing the dynamics of political elections
- Basic optimization problems of economics? Other things from economics? (I don’t know much about these. Are they interesting? Useful?)
- The basic math of neural networks (or “the differential equations for gradient descent in a non-recurrent multilayer network with sigmoid units”) (Eliezer says it’s simper than it sounds, but he was also a literal child prodigy, so I don’t know how much that counts for.)
- Basic statistics
- Whatever the foundations of bayesianism are
- Information theory?
- Decision theory
- Game theory (does this even involve math?)
- Probability theory
- Things from physics? (While I like physics, I don’t think learning more of it would significantly improve my understanding of macro-level processes that that would impact my decisions. It's not as interesting to me as some of the other things on this list, right now. Tell me if I'm wrong or what particular sub-fields of physics are most worthwhile.)
- Some common computer science algorithms (What are these?)
- The math that makes reddit work?
- Is there a math of sociology?
- Chaos theory?
- Musical math
- “Sacred geometry” (an old interest of mine)
- Whatever math is used in meta analyses
- Epidemiology
I’m posting most of these below. Please upvote and downvote to tell me how interesting or useful you think a given topic is. Please don’t vote on how difficult they are, that’s a different metric that I want to capture separately. Please do add your own suggestions and any comments on each of the topics.
Note: looking around, I fount this. If you’re interested in this post, go there. I’ll be starting with it.
Edit: I looking at the page, I fear that putting a sort of "vote" in the comments might subtlety dissuade people from commenting and responding in the usual way. Please don't be dissuaded. I want your ideas and comments and explicitly your own suggestions. Also, I have a karma sink post under
Edit2: If you know of the specific major equations, problems, theorems, or algorithms that relate to a given subject, please list them. For instance, I just added Price's Equation as a comment to the listed "math of natural selection and evolution" and the Median Voter Theorem has been listed under "the math of politics."
MIRI Research Guide
We've recently published a guide to MIRI's research on MIRI's website. It overviews some of the major open problems in FAI research, and provides reading lists for those who want to get familiar with MIRI's technical agenda.
This guide updates and replaces the MIRI course list that started me on the path of becoming a MIRI researcher over a year ago. Many thanks to Louie Helm, who wrote the previous version.
This guide is a bit more focused than the old course list, and points you not only towards prerequisite textbooks but also towards a number of relevant papers and technical reports in something approximating the "appropriate order." By following this guide, you can get yourself pretty close to the cutting edge of our technical research (barring some results that we haven't written up yet). If you intend to embark on that quest, you are invited to let me know; I can provide both guidance and encouragement along the way.
I've reproduced the guide below. The canonical version is at intelligence.org/research-guide, and I intend to keep that version up to date. This post will not be kept current.
Finally, a note on content: the guide below discusses a number of FAI research subfields. The goal is to overview, rather than motivate, those subfields. These sketches are not intended to carry any arguments. Rather, they attempt to convey our current conclusions to readers who are already extending us significant charity. We're hard at work producing a number of documents describing why we think these particular subfields are important. (The first was released a few weeks ago, the rest should be published over the next two months.) In the meantime, please understand that the research guide is not able nor intended to provide strong motivation for these particular problems.
Friendly AI theory currently isn't about implementation, it's about figuring out how to ask the right questions. Even if we had unlimited finite computing resources and a solid understanding of general intelligence, we still wouldn't know how to specify a system that would reliably have a positive impact during and after an intelligence explosion. Such is the state of our ignorance.
For now, MIRI's research program aims to develop solutions that assume access to unbounded finite computing power, not because unbounded solutions are feasible, but in the hope that these solutions will help us understand which questions need to be answered in order to the lay the groundwork for the eventual specification of a Friendly AI. Hence, our current research is primarily in mathematics (as opposed to software engineering or machine learning, as many expect).
This guide outlines the topics that one can study to become able to contribute to one or more of MIRI’s active research areas.
Wikipedia articles from the future
Speculation is important for forecasting; it's also fun. Speculation is usually conveyed in two forms: in the form of an argument, or encapsulated in fiction; each has their advantages, but both tend to be time-consuming. Presenting speculation in the form of an argument involves researching relevant background and formulating logical arguments. Presenting speculation in the form of fiction requires world-building and storytelling skills, but it can quickly give the reader an impression of the "big picture" implications of the speculation; this can be more effective at establishing the "emotional plausibility" of the speculation.
I suggest a storytelling medium which can combine attributes of both arguments and fiction, but requires less work than either. That is the "wikipedia article from the future." Fiction written by inexperienced sci-fi writers tends to generate into a speculative encyclopedia anyways--why not just admit that you want to write an encyclopedia in the first place? Post your "Wikipedia articles from the future" below.
Simulation argument meets decision theory
Person X stands in front of a sophisticated computer playing the decision game Y which allows for the following options: either press the button "sim" or "not sim". If she presses "sim", the computer will simulate X*_1, X*_2, ..., X*_1000 which are a thousand identical copies of X. All of them will face the game Y* which - from the standpoint of each X* - is indistinguishable from Y. But the simulated computers in the games Y* don't run simulations. Additionally, we know that if X presses "sim" she receives a utility of 1, but "not sim" would only lead to 0.9. If X*_i (for i=1,2,3..1000) presses "sim" she receives 0.2, with "not sim" 0.1. For each agent it is true that she does not gain anything from the utility of another agent despite the fact she and the other agents are identical! Since all the agents are identical egoists facing the apparently same situation, all of them will take the same action.
Now the game starts. We face a computer and know all the above. We don't know whether we are X or any of the X*'s, should we now press "sim" or "not sim"?
EDIT: It seems to me that "identical" agents with "independent" utility functions were a clumsy set up for the above question, especially since one can interpret it as a contradiction. Hence, it might be better to switch to identical egoists whereas each agent only cares about her receiving money (linear monetary value function). If X presses "sim" she will be given 10$ (else 9$) in the end of the game; each X* who presses "sim" receives 2$ (else 1$), respectively. Each agent in the game wants to maximize the expected monetary value they themselves will hold in their own hand after the game. So, intrinsically, they don't care how much money the other copies make.
To spice things up: What if the simulation will only happen a year later? Are we then able to "choose" which year it is?
Please Don't Fight the Hypothetical
It is a common part of moral reasoning to propose hypothetical scenarios. Whether it is our own Torture v. Specks or the more famous Trolley problem, asking these types of questions helps the participants formalize and understand their moral positions. Yet one common response to hypothetical scenarios is to challenge some axiom of the problem. This article is a request that people stop doing that, and an explanation of why this is an error.
First, a brief digression into law, which is frequently taught using hypothetical questioning. Under the Model Penal Code:
A person acts knowingly with respect to a material element of an offense when:
(i) if the element involves the nature of his conduct or the attendant
circumstances, he is aware that his conduct is of that nature or that such
circumstances exist; and
(ii) if the element involves a result of his conduct, he is aware that it is
practically certain that his conduct will cause such a result.
Hypothetical: If Bob sets fire to a house with Charlie inside, killing Charlie, is Bob guilty of knowing killing of Charlie? Bob genuinely believes throwing salt over one's shoulder when one sets a building on fire protects all the inhabitants and ensures that they will not be harmed - and did throw salt over his shoulder in this instance.
Let us take it as a given that setting someone on fire is practically certain to kill them. Nonetheless, Bob did not knowingly kill Charlie because Bob was not aware of the consequence of his action. Bob had a false belief that prevented him from having the belief required under the MPC to show knowledge.
The obvious response here is that, in practice, the known facts will lead to Bob's conviction of the crime at trial. This is irrelevant. Bob will be convicted at trial because the jury will not believe Bob's asserted belief was true. Unless Bob is insane or mentally deficient, the jury would be right to disbelieve Bob. But that missed the point of the hypothetical.
The purpose of the hypothetical is to distinguish between one type of mental state and a different type of mental state. If you don't understand that Bob is innocent of knowing killing if he truly believed that Charlie was safe, then you don't understand the MPC definition of knowing. Discussion of how mental states are proven at real trials, or whether knowing killing should be the only criminal statute about killing are different topics. Talking about those topics will not help you understand the MPC definition of knowing. Talking about those other topics is functionally identical to saying that you don't care about understanding the MPC definition of knowing.
Likewise, people who responds to the Trolley problem by saying that they would call the police are not talking about the moral intuitions that the Trolley problem intends to explore. There's nothing wrong with you if those problems are not interesting to you. But fighting the hypothetical by challenging the premises of the scenario is exactly the same as saying, "I don't find this topic interesting for whatever reason, and wish to talk about something I am interested in."
In short, fighting the premises of a hypothetical scenario is changing the topic to focus on something different than topic of conversation intended by the presenter of the hypothetical question. When changing the topic is appropriate is a different discussion, but it is obtuse to fail to notice that one is changing the subject.
Edit: My thesis "Notice and Justify changing the subject," not "Don't change the subject."
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