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:

1. Post the title of your favorite textbook on a given subject.
2. You must have read at least two other textbooks on that same subject.
3. 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...

Like The Cognitive Science of Rationality, this is a post for beginners. Send the link to your friends!

Science is broken. We know why, and we know how to fix it. What we lack is the will to change things.

In 2005, several analyses suggested that most published results in medicine are false. A 2008 review showed that perhaps 80% of academic journal articles mistake "statistical significance" for "significance" in the colloquial meaning of the word, an elementary error every introductory statistics textbook warns against. This year, a detailed investigation showed that half of published neuroscience papers contain one particular simple statistical mistake.

Also this year, a respected senior psychologist published in a leading journal a study claiming to show evidence of precognition. The editors explained that the paper was accepted because it was written clearly and followed the usual standards for experimental design and statistical methods.

Science writer Jonah Lehrer asks: "Is there something wrong with the scientific method?"

Yes, there is.

This shouldn't be a surprise. What we currently call "science" isn't the best method for uncovering nature's secrets; it's just the first set of methods we've collected that wasn't totally useless like personal anecdote and authority generally are.

As time passes we learn new things about how to do science better. The Ancient Greeks practiced some science, but few scientists tested hypotheses against mathematical models before Ibn al-Haytham's 11th-century Book of Optics (which also contained hints of Occam's razor and positivism). Around the same time, Al-Biruni emphasized the importance of repeated trials for reducing the effect of accidents and errors. Galileo brought mathematics to greater prominence in scientific method, Bacon described eliminative induction, Newton demonstrated the power of consilience (unification), Peirce clarified the roles of deduction, induction, and abduction, and Popper emphasized the importance of falsification. We've also discovered the usefulness of peer review, control groups, blind and double-blind studies, plus a variety of statistical methods, and added these to "the" scientific method.

In many ways, the best science done today is better than ever — but it still has problems, and most science is done poorly. The good news is that we know what these problems are and we know multiple ways to fix them. What we lack is the will to change things.

This post won't list all the problems with science, nor will it list all the promising solutions for any of these problems. (Here's one I left out.) Below, I only describe a few of the basics.

Abstract: "Close-call counterfactuals", claims of what could have almost happened but didn't, can be used to either defend a belief or to attack it. People have a tendency to reject counterfactuals as improbable when those counterfactuals threaten a belief (the "I was not almost wrong" defense), but to embrace counterfactuals that support a belief (the "I was almost right" defense). This behavior is the strongest in people who score high on a test for need for closure and simplicity. Exploring counterfactual worlds can be used to reduce overconfidence, but it can also lead to logically incoherent answers, especially in people who score low on a test for need for closure and simplicity.

”I was not almost wrong”

Dr. Zany, the Nefarious Scientist, has a theory which he intends to use to achieve his goal of world domination. ”As you know, I have long been a student of human nature”, he tells his assistant, AS-01. (Dr. Zany has always wanted to have an intelligent robot as his assistant. Unfortunately, for some reason all the robots he has built have only been interested in eradicating the color blue from the universe. And blue is his favorite color. So for now, he has resorted to just hiring a human assistant and referring to her with a robot-like name.)

”During my studies, I have discovered the following. Whenever my archnemesis, Captain Anvil, shows up at a scene, the media will very quickly show up to make a report about it, and they prefer to send the report live. While this is going on, the whole city – including the police forces! - will be captivated by the report about Captain Anvil, and neglect to pay attention to anything else. This happened once, and a bank was robbed on the other side of the city while nobody was paying any attention. Thus, I know how to commit the perfect crime – I simply need to create a diversion that attracts Captain Anvil, and then nobody will notice me. History tells us that this is the inevitable outcome of Captain Anvil showing up!”

But to Dr. Zany's annoyance, AS-01 is always doubting him. Dr. Zany has often considered turning her into a brain-in-a-vat as punishment, but she makes the best tuna sandwiches Dr. Zany has ever tasted. He's forced to tolerate her impundence, or he'll lose that culinary pleasure.

”But Dr. Zany”, AS-01 says. ”Suppose that some TV reporter had happened to be on her way to where Captain Anvil was, and on her route she saw the bank robbery. Then part of the media attention would have been diverted, and the police would have heard about the robbery. That might happen to you, too!”

Dr. Zany's favorite belief is now being threatened. It might not be inevitable that Captain Anvil showing up will actually let criminals elsewhere act unhindered! AS-01 has presented a plausible-sounding counterfactual, ”if a TV reporter had seen the robbery, then the city's attention had been diverted to the other crime scene”. Although the historical record does not show that Dr. Zany's theory would have been wrong, the counterfactual suggests that he might be almost wrong.

There are now three tactics that Dr. Zany can use to defend his belief (warrantedly or not):

1. Challenge the mutability of the antecedent. Since AS-01's counterfactual is of the form ”if A, then B”, Dr. Zany could question the plausibility of A.

”Baloney!” exclaims Dr. Zany. ”No TV reporter could ever have wandered past, let alone seen the robbery!”

That seems a little hard to believe, however.

2. Challenge the causal principles linking the antecedent to the consequent. Dr. Zany is not logically required to accept the ”then” in ”if A, then B”. There are always unstated background assumptions that he can question.

”Humbug!” shouts Dr. Zany. ”Yes, a reporter could have seen the robbery and alerted the media, but given the choice of covering such a minor incident and continuing to report on Captain Anvil, they would not have cared about the bank robbery!”

3. Concede the counterfactual, but insist that it does not matter for the overall theory.

”Inconceivable!” yelps Dr. Zany. ”Even if the city's attention would have been diverted to the robbery, the robbers would have escaped by then! So Captain Anvil's presence would have allowed them to succeed regardless!”

Empirical work suggests that it's not only Dr. Zany who wants to stick to his beliefs. Let us for a moment turn our attention away from supervillains, and look at professional historians and analysts of world politics. In order to make sense of something as complicated as world history, experts resort to various simplifying strategies. For instance, one explanatory schema is called neorealist balancing. Neorealist balancing claims that ”when one state threatens to become too powerful, other states coalesce against it, thereby preserving the balance of power”. Among other things, it implies that Hitler's failure was predetermined by a fundemental law of world politics.

Previously in series: Rationality Verification

From when I was still forced to attend, I remember our synagogue's annual fundraising appeal.  It was a simple enough format, if I recall correctly.  The rabbi and the treasurer talked about the shul's expenses and how vital this annual fundraise was, and then the synagogue's members called out their pledges from their seats.

Straightforward, yes?

Let me tell you about a different annual fundraising appeal.  One that I ran, in fact; during the early years of a nonprofit organization that may not be named.  One difference was that the appeal was conducted over the Internet.  And another difference was that the audience was largely drawn from the atheist/libertarian/technophile/sf-fan/early-adopter/programmer/etc crowd.  (To point in the rough direction of an empirical cluster in personspace.  If you understood the phrase "empirical cluster in personspace" then you know who I'm talking about.)

I crafted the fundraising appeal with care.  By my nature I'm too proud to ask other people for help; but I've gotten over around 60% of that reluctance over the years.  The nonprofit needed money and was growing too slowly, so I put some force and poetry into that year's annual appeal.  I sent it out to several mailing lists that covered most of our potential support base.

And almost immediately, people started posting to the mailing lists about why they weren't going to donate.  Some of them raised basic questions about the nonprofit's philosophy and mission.  Others talked about their brilliant ideas for all the other sources that the nonprofit could get funding from, instead of them.  (They didn't volunteer to contact any of those sources themselves, they just had ideas for how we could do it.)

Now you might say, "Well, maybe your mission and philosophy did have basic problems—you wouldn't want to censor that discussion, would you?"

Hold on to that thought.

Because people were donating.  We started getting donations right away, via Paypal.  We even got congratulatory notes saying how the appeal had finally gotten them to start moving.  A donation of $111.11 was accompanied by a message saying, "I decided to give **** a little bit more.  One more hundred, one more ten, one more single, one more dime, and one more penny.  All may not be for one, but this one is trying to be for all."

But none of those donors posted their agreement to the mailing list.  Not one.