I once believed that six times one is one.

I don't remember how it came up in conversation, but for whatever reason numbers became relevant and I clearly and directly stated my false belief. It was late, we were driving back from a long hard chess tournament, and I evidently wasn't thinking clearly. I said the words "because of course six times one is one." Everyone thought for a second and someone said "no it's not." Predictable reactions occurred from there.

The reason I like the anecdote is because I reacted exactly the same way I would today if someone corrected me when I said that six times one is six. I thought the person who corrected me must be joking; he knows math and couldn't possibly be wrong about something that obvious. A second person said that he's definitely not joking. I thought back to the sequences, specifically the thing about evidence to convince me I'm wrong about basic arithmetic. I ran through some math terminology in my head: of course six times one is one; any number times one is one. That's what a multiplicative identity means. In my head, it was absolutely clear that 6x1=1, this is required for what I know of math to fit together, and anything else is completely logically impossible.

It probably took a good fifteen seconds from me being called out on it before I got appropriately embarrassed.

This anecdote is now my favorite example of the important lesson that from the inside, being wrong feels exactly like being right.

The belief was minor, but the story is entertaining:

A while ago a guy walked into the bookstore and asked me for a copy of The Art of War—by Machiavelli.

I've developed the habit of being polite when customers are mistaken about details, taking (and often inventing) every possible opportunity to help them save face, so I handed him a copy of Sun Tzu without comment—though you can be sure that internally I was feeling all kinds of smug at the chance to display my superior knowledge of extremely common classic books. He glanced at it and left—mortified, I imagined.

A few months later, I looked it up and discovered that Machiavelli did, in fact, write a treatise called The Art of War.

But that isn't the embarrassing part.

The embarrassing part is that, in the moment I went to check, what I was thinking was not "Hmm, I wonder if I could have been mistaken"; it was "Heh, I wonder if anyone else has made the same mistake as that idiot!" My error was corrected only incidentally—in the course of my efforts to reinforce it.

Before I started tutoring I believed that anyone can learn first year math and science if only they put in the time and effort. Before I went to grad school I believed that I can learn all the advanced math and theoretical physics topics I was interested in. Neither belief survived experimental testing.

I used to think Narwhals were fictional animals. And people telling me they were real were just joking. It wasn't until HS that I was convinced they actually existed. My mental process was like "No way are there aqua unicorns."

Semi-political: I used to believe the correlation between economic freedom and economic growth was much stronger than it is. (I know there is no canonical choice of measurement for either variable). This realization had pretty important consequences for me.

My estimates of public opinion surveys were totally wrong. On almost every issue (sexuality, morality, politics, etc) I was completely wrong about the distribution of beliefs. Given my history of failure in this domain I no longer really on my own "intuitive" estimates of the distribution of group beliefs. Instead I seek explicit surveys.

False belief: That in the U.S. the death penalty was cheaper than life in prison.

Believing this wasn't rational. I didn't take such basic steps as looking up the costs surrounding executions or life imprisonment. Executions get much more appeals, trials and legal attention.

False belief: That in the U.S. deaths by firearm are generally homicides, not suicides.

Believing this also wasn't rational. I didn't take such basic steps as looking up available death statistics.

Actually, looking through things potentially on the list for me, a lot of them seem to have the following general form:

1: Something is asserted.

2: I think: 'Yeah, that sounds plausible.'

3: I don't bother to look up any data about it, I just move myself to the believe column.

4: Later, someone else reports data about it.

5: I'm surprised that my earlier beliefs were wrong.

I've since became more skeptical of believing things based on just assertions, (I can even recall a recent instance where an assertion popped up on TV which my wife believed, but which I was skeptical of and which upon looking it up we found data didn't support it and that they were massively overstating their case)

But I can definitely recall beliefs that I have had in the past that were fundamentally just assertion based and the followed the above pattern.

One of the slides of my physiology 102 course consisted of the claim that women blink twice as much as men. I put that as a fact into Anki. Now it turns out that when I google around it isn't true.

In general the heuristic of believing things I'm told in science university lectures isn't completely bad, but it seems that there a category where lectures want to mention interesting facts and then tell students interesting facts that aren't necessarily true.

My own example: I used to be a pretty strong believer in the strong crisis version of peak oil. This was mainly because I was around people who were; I went along with fairly naive trend extrapolation (exponential resource use increase, hard to develop new resources).

Eventually, around 2012 or so after oil prices had spiked then dropped then risen again and shale oil was a thing, I tempered my ideas, and took the much more rational view that oil wouldn't have a crisis-like peak, more a plateau. I believed that extremely high oil prices could drive massive adoption of much more advanced drilling methods. Therefore there would never be a crisis of extraordinary oil scarcity, but we could very well face $200/bbl oil (which we'd learn to live with like $140/bbl oil). But I didn't believe oil would really drop; I was bullish on almost all resource prices and on developing nation growth driving them.

While this was founded in a better understanding of economics and the petroleum industry, it was still grounded in false assumptions of continuing high-pace developing world growth and pessimism about alternative energy. Oil has now plummeted to $80/bbl, which I never expected to see again in my lifetime.

For some fun examples, see wikipedia's list of common misconceptions, (although several entries seem like misconceptions about misconceptions.)

I once believed that most people have a basic understanding of how Solar system works. My belief in humanity shattered when during a discussion with with several graduates of physics (!) I discovered that most of them do not know what is the orbital period of Moon. An impromptu survey revealed that about 8 people from 10 thought it was one day or one week. One knew, one even asked if I want to know sideric or synodic period.

After Sandy Hook, I got angry and convinced guns rights people and the NRA were nuts.

Then I looked at the data for gun deaths in the US and I seem to remember mass shootings are a statistical anomaly. Handguns in 1-on-1 killings are the bulk of the problem.

Then I considered the second amendment and how maybe it's not a terrible idea to have an armed populace should the gov't get corrupt and motivated to oppress. Also, I saw a TED talk that had me convinced income inequality was the cause of gun (and all sorts of) violence, and concluded gun ownership rates (and gun enthusiasm) weren't to blame for anything.

Then I thought an armed populace wouldn't matter against a sufficiently armed gov't. Then I was like, "What do I know about such matters??"

Then I extrapolated this revelation about my ignorance out to include everything, and I recognized I have no idea what to believe about gun rights, or anything else.

Then I went on FB and started arguing with gun enthusiasts, because they seem wrong to all the rational parts of me.

Then back to LW, to sort out my bad epistemological habits...

I think this was a great idea for a post. If LessWrong rationality is worthwhile, then it ought to get lots of replies on concrete facts - not moral preferences, theology, or other unproveables.

I used to believe that embryos pass through periods of development representing earlier evolutionary stages - that there was a period when a human baby was basically a fish, then later an amphibian, and so on. I believed this because my father told me so; he was a doctor (though not an obstetrician), and the information he had given me about other subjects was highly reliable. Most knowledge is second hand - it was highly rational for me to believe him. I now know (also second hand!) that Haeckel's ideas were debunked a long time ago - although they might well have been in a textbook when my father was at medical school.

To me, the lesson is trust, but verify.

When I went to the London meetup, someone mentioned the "punching someone upward in the nose can send the nosebone into the brain and kill them" urban myth, and we all nodded except the one guy who actually bothered to think about it and said "I don't think that can be right, it doesn't make evolutionary sense" or something on those lines. I think, in my case at least, this was "just" a cached thought from childhood, but it was quite humbling how many of us got something so simple so wrong.

I used to believe that altruism was generally faked. This was based on my direct experience (and perhaps some mind projection fallacy), and an assumption that personalities were consistent over time, or perhaps situation - so probably the good old fundamental attribution error. And a default assumption that high schools couldn't really just be terrible, because no-one would allow that to happen. Why did I believe that? I think not appreciating how fallible memory is, and overestimating the engineering of the human reasoning apparatus. Evolution is always stranger than you think.

I used to not believe in quantum mechanics or general relativity, because they were terribly explained. I guess again I was assuming too much good faith on the part of educators. In retrospect if I'd just found a college textbook I'd've straightened myself out a lot sooner than I did. The popular science publishing industry still seems dysfunctional, but presumably there are incentives that I don't appreciate that keep it the way it is.

I believed that the composition of a rational rotation of a sphere and another rational rotation of a sphere will be rational. (By a rational rotation I mean a rotation of a sphere around some axis which in radians is a rational multiple of pi, and thus will end up putting the sphere back where it started if you apply it enough.) Counterexample: Two 30 degree rotations each around a different axis with the two axies perpendicular to each other. I believed this because I was too used to thinking about the two-dimensional case, where it is trivially true.

Until very recently, I was convinced that it was extremely unlikely that any form of adiabatic quantum computing would have any chance at working at providing speedups, either asymptotically or practically. This belief came to a large extent as what was in retrospect an irrational reaction to the junk and bad hype that has been repeatedly coming from D-Wave. I changed my position when Scott Aaronson made this comment (comment number 25).

More mind-killing territory: Until about 3 days ago, I was convinced that claims that mass shootings were increasing in the US were due purely to media scare tactics and general human tendencies to see things as getting worse. This article made me strongly update against that. Since then, I've seen this response and this one which were both deeply unpersuasive as responses go.

Even more potential mindkilling: Having read more of Slatestarcodex, I've become convinced that he's correct that there really is a substantial fraction of what self-identifies as the "social justice" movement, primarily in an online context, that really is toxic, and that the rest of the left and the serious, sane part of the SJers aren't doing enough to call them out on it. On the flipside, "Gamergate" has convinced me that there's still a very real need for a vocal feminist movement, and that latent misogyny is still pretty common. Edit: To specify what this means in an operational sense, that there are a lot of SJers out there who are making personal attacks or calls for censorship against those with whom they disagree.

I was convinced in 2008 that Obama was going to be good for civil liberties. I don't think I need to discuss in any detail why that was wrong or how I got convinced otherwise, since the reasons should be pretty obvious.

Probably not too interesting, but after studying physics at university I was pretty sure that the Many-Worlds interpretation of QM was crazy-talk (nobody even really mentioned it at uni). Of course I didn't read Eliezer's sequence on QM (although I read the others). I mean I had a degree in physics and Eliezer didn't.

Then after seeing it over and over again on LW, I actually read this paper to see what it was all about. And I was enlightened. Well, I had a short crisis of faith first, then I was enlightened.

This all could have been avoided if I had read that paper earlier. The lesson is that I can't even trust my fellow physicists :(

I used to believe that no one would loot a large organization (especially in the first world) from the top. It took me a while to realize anyone could want that much money.

The comment has five karma points, so I may not be the only person who had that blind spot. I suspect in my case that having grown up slightly upper middle class contributed to my false belief-- it was a combination of comfort/security with limited ambition.

Not so much a false positive belief but a conspicuous failure to fill the blanks in the world model: I didn't realize that the night sky appears to rotate until I was a teenager reading Carl Sagan's Contact, and came to the part where the character is watching the sky at night and the stars are described as moving slowly along the night. Then it was obvious that of course that's what happens, but this was the first time I'd seen anyone say this aloud, and before that I would've just assumed without thinking that stars stay in the same relative place all night.

I vaguely recall believing when I was young that there were no real bisexuals, just gays in denial about it.

I used to think acne was unrelated to diet (other than perhaps via direct facial contact with grease).

When law enforcement first started being equipped with tasers, I thought this was a good thing, because they would use nonlethal force on occasions where they would previously have used firearms. It turned out that police continued to use lethal force as before, and instead used tasers in situations where they might actually have talked people down in the past.

Before coming to LW I intuitively believed in the map/territory distinction (physical realism, if you will). After going through the countless arguments of the type "Is real?" (where can be qualia, consciousness, wavefunction, God or what have you.) I gradually came to the conclusion that the term "real" is both misleading and counterproductive. If a sentence (excepting mathematical statements) cannot be rephrased by replacing "real" or "true" with "accurate", then it is meaningless.

Up next: stop believing in using parentheses so much.