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How to Be Wrong (2016) (mathenchant.wordpress.com)
115 points by JonahBraun 11 days ago | hide | past | web | favorite | 32 comments





Oh man, I'm always glad to hear I'm not the only one who got the Monty Hall problem wrong. Here is my embarrassing MH story.

Like Paul Erdős, I resorted to experimentation. Very much unlike Paul Erdős the computer program I wrote contained a one-off error in its PRNG that coincidentally confirmed the wrong result. I then spent a day or so on Usenet insisting stubbornly on the wrong solution until some very kind person on sci.crypt made a complete truth table as a proof. That exhaustive proof immediately convinced me of my idiocy.

Lesson: If a bunch of smart and educated people tell you that you're wrong, then you're probably wrong.


I embarrassed myself on usenet. Still remember it. Still can...feel it.

It was that problem that made me realize that although physicists deal with probabilities all the time, we don't really understand them.


The thing is that the person who got it right was not a researcher while all those that got it wrong were.

Either way, you should never feel bad about getting the monty hall problem wrong because it was never set up as a fair question. Marilyn Savant made some incredible assumptions about the premise of the question that were never clear and thus almost completely made up the question herself.


> Lesson: If a bunch of smart and educated people tell you that you're wrong, then you're probably wrong.

Not always the case. As they say, science advances one funeral (of smart and educated people) at a time...


There will always be exceptions, hence the "probably" in their lesson. There's paradigm shifts, and then there's an unnoticed bug in code hacked together to prove something to oneself.

I will probably continue to get the Monty Hall problem wrong for the foreseeable future despite understanding the logic. I think the issue with it for me is the difference between probability and calculated probability (which I do not think is a proper mathematical term).

Like...when someone makes reference to a given probability X "changing" from ~33% to ~67%, they are referring to the updated model that we use to calculate the probability. Nothing in reality has changed, but rather the model has.


“If a bunch of smart and educated people...”

Well, you do have to first recognize that the particular bunch is composed of smart and educated people...


As Richard Feynman says, "Some people say, How can you live without knowing? I do not know what they mean. I always live without knowing. That is easy. How you get to know is what I want to know."

I always try to weave some skepticism into my thought process, because you never know when some of your fundamental assumptions can be wrong.


As a CS university lecturer, I acknowledge that there is little room for exploration, and the chance of being wrong, in most assessment schemes. Any mistake loses points and lowers the GPA, so nobody likes to make mistakes, however creative and interesting. Shame. The system cannot be easily revised because the students themselves oppose it. To them it seems intuitively unfair that somehow those who make mistakes may get the same points as those who get it right.

You didn't read their first point - if you're going to be wrong, do so in private. You should be making as many mistakes as possible at home or after hours so that by class or test time you never make them again. Mistakes are a way of learning but not a way of doing. After all, the entirety of life was built with 1 tool - the mistake.

Wait a minute, mistakes are a "way of learning" but you should avoid them in school?

You should avoid them when trying to produce actual good work and results, obviously. Before that point, make as many as you want so you can learn how to produce flawless results.

At my university (UK) only final exams count, and everything before then (such as problem sets) are marked/graded only for feedback, which is a nice middle ground. Requires students motivated enough to submit work that won't count.

>Sometimes something even simpler than the “I used to think so too but now I know better” criterion can be used to unmask bunk; if there’s a good story and one that’s disappointingly banal, usually the latter is the one that’s unfortunately true.

A problem with this is that there are now increasingly more people who automatically opt for the "disappointingly banal" story even in cases when the good story is the actually true one (and insist on it) -- because it enables them to take pride in "debunking" and feel superior to others.

In other words, where once most people went for the "good story" for psychological reasons (because it's more satisfying, makes for interesting talk, etc), now, with the raise of sites like Snopes, "fact-checking" forums, sceptic sites, and so on, there's an increasing equally bogus motive for preferring the banal story.

(And this is orthogonal to Occam's razor. For one, because the banal and the interesting story might be of equal simplicity and with equally few prerequisites. Beside's Occam's razor is just an observation, not an absolute law: sometimes the more elaborate course is indeed what happened).


> even in cases when the good story is the actually true one

I enjoy being a jerk and ruining a story as much as the next person, but you have to check your facts before doing something like that.

Are there any good examples you've come across of someone miscorrecting a "good" story to a banal one?


vos Savant's article on this that lists highlights from the letters:

http://marilynvossavant.com/game-show-problem/


The Monty Hall problem, as it is initially stated by vos Savant (and even in this link) is not well written. It make implicit assumptions about the host behavior.

See https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...

If this had been clear from the beginning, there would not have been so much confusion about this problem. So in this case, vos Savant is also quite "wrong".


Vos Savant claimed that, of the people who explained their demurral, most were, in fact, basing their objections on the intended reading of the question.

It really irks me that the original reader asked the question, stated that the host knew what was behind the doors, but didn't state any rules to the gameshow whatsoever. Savant basically made up the entirety of the question herself.

This whole section of history should just be erased because of how much controversy it caused without any serious progression.


Such a great read.

>I tell my students that, in the first place, they need to get over the fear of making mistakes.

>So my answer to the question “How to be wrong?” is: “Early and often!”

>And if you can’t be genuinely modest, fake it. Develop a habit of always acting in such a way that if you prove to be wrong, it won’t make you look really really bad.

>certain truths may be denied to us unless we pass through a preparatory stage of error.

>For now, I’ll skip ahead to the moral: Sometimes, when you find the right hole, you shouldn’t just put one foot into it. You should jump in with both feet the way Alice did, and see what kind of wonderland it leads to.


"Being Wrong — Adventures in the Margin of Error"; wonderful 2010 book reviewed here by Dan Gilbert: https://www.nytimes.com/2010/07/25/books/review/Gilbert-t.ht...

Wow, I liked it (although none of the Monty Hall story was new to me) until the part where he was disgustingly dismissive and insulting to Semmelweis. Then I stopped reading. A less sympathetic account can hardly be imagined, I thought it was shameful.

It clearly assumes that the reader is aware of the background and simply states that it is "conceivable" that Semmelweis' attitude (whether warranted or not) may have negatively impacted his message. It seems like a sound point; that sort of thing does unfortunately happen.

Semmelweis "the medical pioneer whose unyielding adherence to principles of hygiene may have been responsible for the deaths of millions. Sure, he saved lots of people, but it’s conceivable that the practice of routine hand-washing in surgical theatres might have spread farther, and faster, if the man had never been born (and therefore never antagonized so much of the medical establishment with his rigidity and brusqueness, and therefore never put hand-washing in such bad odor)."

I don't think that saying the writer here 'simply states that it is "conceivable" that Semmelweis' attitude (whether warranted or not) may have negatively impacted his message' is a reasonable interpretation of that passage, to say the least. (I also can't see that it "clearly assumes" what you say it does. You probably wouldn't link to the guy's wikipedia page if you assume people know not only who he is but the background too)

What was his 'attitude'? It drove him nuts that no-one would listen?


A professor at a university I worked at, had such antipathy for the computer centre director who had a personal chair for his non-teaching role, that we were under standing instructions to vote against anything he suggested at a departmental meeting. Yet, both had to agree on significant computing spend for the university. Net result? lose-lose outcomes...

It's interesting to draw a parallel between the author's argument that Semmelweis could have achieved more if he had been more respectful and "never antagonized so much of the medical establishment" to similar arguments continuously leveled at Martin Luther King, Jr. and other civil rights leaders. Despite this same argument being dredged up whenever there's a conflict between reform and inertia, history provides few examples of polite, demur, reformers who were careful to never antagonize the establishment.

It's also worth pointing out that the phrase "it's conceivable that" is a fairly cheap rhetorical trick: you can advance any ludicrous argument with no evidence or material support while forcing anyone who disagrees with you to produce proofs that are beyond all reasonable doubt. "It's conceivable that if the Nazis had won WWII, we would have colonies on the Moon by now." "It's conceivable that Yahoo's stock price will increase ten-fold in the next year." "It's conceivable that eating dog shit is the key to human immortality." Sure, it's conceivable but because it's neither plausible nor likely, and because no valid argument can be advanced to support the claim, it's not worth talking about, unless we're writing alternative history fiction. Yet authors often use this or similar phrases to propose arguments that they personally believe but know they cannot defend.

ajkjk 11 days ago [flagged]

Weird that you would stop reading for that, and announce it here. As if there's some virtue in turning away in disgust.

Don't be snarky

I'm offering a severe criticism of the writer, and sticking up for Semmelweis. I'm not sure what you're doing, besides tempting me to use the phrase 'virtue signalling' for the first time ever.


And article merely offered criticism of Semmelweis approach. Why is that disgusting? Is that untruth or he did not ended in that asylum? Should these topics be taboo?

There is really lesson there, you can alienate people enough so they end up not listening to reasonable parts of what you are pushing for.


>"Semmelweis [...] may have been responsible for the deaths of millions"

How does that not strike you as unnecessarily harsh and unwarranted? The statement reeks of viewing history through the modern lens, and the author doubles down on the next sentence suggesting that the scientific community would have somehow opened their eyes if only Semmelweis had either not been born or had been less of an asshole, or something.


"History through modern lens" seems to be a bit out of topic complaint.

The rest of paragraph explains why author thinks he was wrong. It would be interesting to read historical dispute, but your complaint seems to be less about different interpretation of history and more about making criticism of past personalities taboo.


Be right, from a different point of view.



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