16 ms·

Beware of Cranks: Misguided attempts to solve impossible mathematical problems

49 points by Hooke 7y ago

knzhou 7y ago
I've talked with a bunch of cranks and my experience resonates with this article. I believe in reasoned argument and persuasion, probably to a fault, but I never managed to change any of their opinions in the slightest. One of them had a theory that every electron was made of two photons going round and round. After pointing out a few of the many problems with that he tracked down where I live to try to report me for "censorship".
- throwaway2048 7y ago
  You are only very rarely going to win over somebody committed to an irrational belief (who usually already holds it in plain contradiction to available facts) with logical arguments.
  - girvo 7y ago
    Said simpler: you can use logic to get someone out of a position they didn’t use logic to get into
  - sopooneo 7y ago
    I completely agree. But might some fraction of such people be “won over” by methods other than logic? Asking them how they got interested, perhaps, and drawing out what in their past caused them to become so obsessed? Or even by redefining the goal of the debate? It may be that I’m giving too much credit and most are truly hopeless. But so often with “people problems” I’ve seen approaches work beautifully and which in retrospect seem obvious. But in the moment I would never have thought up because I was considering things so narrowly.
    - knzhou 7y ago
      In my experience, most of these people are over twice my age and slip into condescension the second I stop laying down logical arguments. If I don't argue against them logically, they invariably walk away triumphant, thinking they've just educated some ignorant young man. It makes the problem worse, so I might as well not talk with them at all. In any case, their stories are all remarkably similar...
- incompatible 7y ago
  I think the best way of dealing with nonsense in Internet forums is to give a single reply, and then go away. Getting dragged into an ongoing "discussion" is unlikely to be worth the effort, since such people typically resort to rejecting evidence and making ad hominem attacks.
hprotagonist 7y ago
> 3. They don’t understand what it means for something to be mathematically impossible. This one gets a lot of technically competent people. I spent a very unsatisfying 45 minutes vainly trying to explain to an eminent biologist that no, really, some statements really are _undecidable_ -- and no, that doesn't mean that at some future time we'll figure out a new approach that lets us decide them.
- scott_s 7y ago
  I encountered something similar almost a decade ago on this forum when discussing the halting problem: https://news.ycombinator.com/item?id=1322901 https://news.ycombinator.com/item?id=1322901
- nikanj 7y ago
  Reminds me of an infamous VC story I heard years ago: A bunch of engineers tell him that feature X is impossible due to latency, and the latency is capped by the speed of light. He challenges the team by asking them to speculate about options, if they managed to "disrupt" the industry by breaking that speed barrier, and gets mighty upset by these closed-minded engineers who are unwilling to accept any possibility of a breakthrough
  - yummypaint 7y ago
    Thats when you say sure well start a basic research lab that will be $100 mil per year
  - ahartmetz 7y ago
    It could possibly be a valid question: Think about what it would do for the customer, then see if there are different solutions for some of these things. But I guess that was not how it went.
  - FakeComments 7y ago
    I’m not convinced the speed of light is a barrier when you can build a non-Euclidean quantum computer. Maybe the VC had a point, and the engineers were overly confident in one perspective — one that had assumptions subtly different from reality.
Animats 7y ago
If you can put the points of the compass against the straightedge, which gives you a marked straightedge, you can trisect an angle. But that's considered cheating. Archimedes is credited with figuring out this approach.
paultopia 7y ago
Super curious---I actually never took trig (complicated story), so I don't understand the trisecting an angle thing at all. What is it that makes measuring the angle and then dividing that measurement by 3 impossible?
- pkd 7y ago
  It's not the actual measurement, it's the physical act of dividing an angle graphically into thirds using nothing but a compass and a ruler.
- kryptn 7y ago
  While dividing by three is easy, dividing an angle by three with just a compass and a straight edge is impossible. Numberphile[1] did a video on this a few years ago [1] https://www.youtube.com/watch?v=6Lm9EHhbJAY https://www.youtube.com/watch?v=6Lm9EHhbJAY (Euclid's Big Problem - Numberphile)
- recursive 7y ago
  "Measuring" is not permitted. You are granted access only to an idealized compass and straight edge. There's a mobile game called Euclidea based on this which I'd recommend.
  - paultopia 7y ago
    Oooh. I was imagining a compass like you're given in school, with labels on it, and ditto a ruler. :-)
    - SamReidHughes 7y ago
      That would be a protractor, which would be allowed if there were 340 degrees in a circle.
- throwaway2048 7y ago
  An important aspect of this isn't that you cant trisect any particular angle, its that you cant trisect any arbitrary angle, plenty of angles, like 90 degrees, are trivial to trisect.
te_platt 7y ago
I agree with the main argument but would like to note "crank" in not an all or nothing description. Sometimes the problem as publicized doesn't exactly match the precise problem. For example you can trisect an arbitrary angle if allowed an infinite number of steps. Sometimes the problem is in breaking the abstraction layer. For example one of my kids thought you could make arbitrarily slow motion videos by taking slow motion videos of slow motion videos. And that brings up the issue of how to handle a crank. I loved that my son thought through the video issue and didn't want to inhibit future thinking. We ran some experiments taking video of the tv and it was fun. Sometimes people won't accept counter arguments and evidence (sometimes that person is me) and there's a time to move on. Still, in my experience few people are true die hard cranks and most people respond well if given the right direction.
dekhn 7y ago
http://norvig.com/beal.html http://norvig.com/beal.html Peter told me he often gets candidate solutions that the sender hasn't even validated.
schoen 7y ago
I used to answer correspondence for the EFF Cooperative Computing Awards (which are an actual financial prize for finding very large primes) and people who wrote in were almost uniformly either kids or people meeting all of the criteria mentioned here. Almost none of them thought it was important to understand any prior results about primality testing before submitting a claim for the prize, while a majority didn't seem comfortable with the idea of a mathematical proof or theorem. In general, they didn't have a sense that some properties are always true, some are never true, and some are sometimes true and sometimes not true, and that mathematical reasoning can often definitively establish which of these categories a particular property is in.
secraetomani 7y ago
> In fact, members of the academy were so tired of being inundated with quackery that in 1775 they passed a resolution not to accept solutions to the problems of circle squaring, angle trisection, or cube doubling. This is hilarious.
vector_spaces 7y ago
While many people who become preoccupied with "problems" like these are operating in bad-faith and can't be swayed otherwise, I would be very surprised if a large number of them (if not most of them) weren't just lay people who were simply curious, who had poor experiences learning math or technical subjects growing up, and for once read about some mathematical "problem" that was accessible to them, were excited by it, and set about exploring it not realizing it was actually a red herring. And unfortunately, if you lack a good foundation, you won't be able to realize the "problem" you're working on is actually a red-herring, and the rabbit holes you wander through when researching these "problems" will just teach you further bad habits and crankery. For the sake of those people, I don't think it's fair or right to immediately assume bad faith and take the attitude of "run for the hills" when met with anyone who's gone down such a path. And I don't think it's right to make a mockery of them either (except of course for the ones that start trying to write books, teach seminars, or submit papers about their "discoveries" without ever getting it right). Instead maybe we can point them towards resources so they can fix their faulty foundation and find more productive ones? No need to engage them further. Just give them something -- even something canned -- to sate the obvious curiosity that they have and give them a little direction. At the very least we can not mock them and assume bad faith -- there's nothing wrong with being curious.
- rabidrat 7y ago
  A "crank" is a very specific type of person, who will not heed any constructive criticism and in fact deliberately avoids resources from the establishment. Any dismissal is viewed as a conspiracy by the establishment to keep their brilliant ideas from dismantling the establishment's sacred cows. Like concern trolls, their goal is seemingly to waste the time and energy of anyone willing to listen or engage, except they're not doing it wittingly, so you just wind up feeling like a jerk when you inevitably have to ignore their latest 20-page ramble and get some real work done.
- knzhou 7y ago
  As they say, sounds good, doesn't work. You can tell the genuinely curious sort from true cranks at a glance, and this article is about the latter. Every academic has interacted with far too many true cranks. I always try to give rebuttals that are accessible, explaining in plain English what is going wrong and giving resources for follow-up learning. It doesn't work -- you get "that's cute, you still believe in textbooks, when I've proven them all wrong."
rdc12 7y ago
I wonder if Andrew Wiles had taken a different approach when announcing he had solved Fermat's Last Theorem if he would have been considered a crank. I would imagine that problem would have attracted nonsense solutions prior.
- anyfoo 7y ago
  That's a big hypothetical, though. Andrew Wiles had been producing sensible mathematics in the community already, so there was no reason to suspect him of being a crank. Also, his proof did not emerge in a vacuum, he pursued approaches that were already known to be connected to FLT. As for FLT attracting nonsense solutions: Yes, plenty of them. It being such a simply stated problem, and immediately understandable to laypeople certainly exacerbated the problem.
  - rdc12 7y ago
    Fair point I have no familiarity with his earlier work, or even that there was suspicion of a connection, I did mean for my point to be a bit more general, just seemed like a reasonable example
thecopyeditor 7y ago
A long time ago, I spent the summer at my university where I was a mathematics major. I needed a job to pay for groceries, so I took a part time copy editing job at the math journal. We got at least one "whack job" paper a week. Bear in mind this was when the internet was first getting traction, so I knew some of these guys from usenet… lol
Semiapies 7y ago
See also this site on weekends, when every "physics revolution" and "fix" for dark matter in cosmology gets posted.about. A rare genuinely obligatory xkcd: https://xkcd.com/1758 https://xkcd.com/1758
breck 7y ago
"Beware of Cranks" shows a terrible understanding of how major progress in science and technology happens. If you go around flipping the "crank bit", sure, you will save yourself spending time evaluating lots of correct negatives and have more time to make on incremental progress, but you will also have a couple of false negatives, one or two of which will go on to change the world. World change is dominated by black swans. Conversely, Thiel's Hereticon conference idea is brilliant and shows a terrific understanding of how progress in science happens.
dang 7y ago
A previous discussion of Underwood Dudley's classic article: https://news.ycombinator.com/item?id=14446708 https://news.ycombinator.com/item?id=14446708

49 points by Hooke 7y ago

I've talked with a bunch of cranks and my experience resonates with this article. I believe in reasoned argument and persuasion, probably to a fault, but I never managed to change any of their opinions in the slightest. One of them had a theory that every electron was made of two photons going round and round. After pointing out a few of the many problems with that he tracked down where I live to try to report me for "censorship".

throwaway2048 7y ago
You are only very rarely going to win over somebody committed to an irrational belief (who usually already holds it in plain contradiction to available facts) with logical arguments.
- girvo 7y ago
  Said simpler: you can use logic to get someone out of a position they didn’t use logic to get into
- sopooneo 7y ago
  I completely agree. But might some fraction of such people be “won over” by methods other than logic? Asking them how they got interested, perhaps, and drawing out what in their past caused them to become so obsessed? Or even by redefining the goal of the debate? It may be that I’m giving too much credit and most are truly hopeless. But so often with “people problems” I’ve seen approaches work beautifully and which in retrospect seem obvious. But in the moment I would never have thought up because I was considering things so narrowly.
  - knzhou 7y ago
    In my experience, most of these people are over twice my age and slip into condescension the second I stop laying down logical arguments. If I don't argue against them logically, they invariably walk away triumphant, thinking they've just educated some ignorant young man. It makes the problem worse, so I might as well not talk with them at all. In any case, their stories are all remarkably similar...
incompatible 7y ago
I think the best way of dealing with nonsense in Internet forums is to give a single reply, and then go away. Getting dragged into an ongoing "discussion" is unlikely to be worth the effort, since such people typically resort to rejecting evidence and making ad hominem attacks.

hprotagonist 7y ago

> 3. They don’t understand what it means for something to be mathematically impossible. This one gets a lot of technically competent people. I spent a very unsatisfying 45 minutes vainly trying to explain to an eminent biologist that no, really, some statements really are _undecidable_ -- and no, that doesn't mean that at some future time we'll figure out a new approach that lets us decide them.

scott_s 7y ago
I encountered something similar almost a decade ago on this forum when discussing the halting problem: https://news.ycombinator.com/item?id=1322901 https://news.ycombinator.com/item?id=1322901
nikanj 7y ago
Reminds me of an infamous VC story I heard years ago: A bunch of engineers tell him that feature X is impossible due to latency, and the latency is capped by the speed of light. He challenges the team by asking them to speculate about options, if they managed to "disrupt" the industry by breaking that speed barrier, and gets mighty upset by these closed-minded engineers who are unwilling to accept any possibility of a breakthrough
- yummypaint 7y ago
  Thats when you say sure well start a basic research lab that will be $100 mil per year
- ahartmetz 7y ago
  It could possibly be a valid question: Think about what it would do for the customer, then see if there are different solutions for some of these things. But I guess that was not how it went.
- FakeComments 7y ago
  I’m not convinced the speed of light is a barrier when you can build a non-Euclidean quantum computer. Maybe the VC had a point, and the engineers were overly confident in one perspective — one that had assumptions subtly different from reality.

Animats 7y ago

If you can put the points of the compass against the straightedge, which gives you a marked straightedge, you can trisect an angle. But that's considered cheating. Archimedes is credited with figuring out this approach.

paultopia 7y ago

Super curious---I actually never took trig (complicated story), so I don't understand the trisecting an angle thing at all. What is it that makes measuring the angle and then dividing that measurement by 3 impossible?

pkd 7y ago
It's not the actual measurement, it's the physical act of dividing an angle graphically into thirds using nothing but a compass and a ruler.
kryptn 7y ago
While dividing by three is easy, dividing an angle by three with just a compass and a straight edge is impossible. Numberphile[1] did a video on this a few years ago [1] https://www.youtube.com/watch?v=6Lm9EHhbJAY https://www.youtube.com/watch?v=6Lm9EHhbJAY (Euclid's Big Problem - Numberphile)
recursive 7y ago
"Measuring" is not permitted. You are granted access only to an idealized compass and straight edge. There's a mobile game called Euclidea based on this which I'd recommend.
- paultopia 7y ago
  Oooh. I was imagining a compass like you're given in school, with labels on it, and ditto a ruler. :-)
  - SamReidHughes 7y ago
    That would be a protractor, which would be allowed if there were 340 degrees in a circle.
throwaway2048 7y ago
An important aspect of this isn't that you cant trisect any particular angle, its that you cant trisect any arbitrary angle, plenty of angles, like 90 degrees, are trivial to trisect.

te_platt 7y ago

I agree with the main argument but would like to note "crank" in not an all or nothing description. Sometimes the problem as publicized doesn't exactly match the precise problem. For example you can trisect an arbitrary angle if allowed an infinite number of steps. Sometimes the problem is in breaking the abstraction layer. For example one of my kids thought you could make arbitrarily slow motion videos by taking slow motion videos of slow motion videos. And that brings up the issue of how to handle a crank. I loved that my son thought through the video issue and didn't want to inhibit future thinking. We ran some experiments taking video of the tv and it was fun. Sometimes people won't accept counter arguments and evidence (sometimes that person is me) and there's a time to move on. Still, in my experience few people are true die hard cranks and most people respond well if given the right direction.

dekhn 7y ago

http://norvig.com/beal.html http://norvig.com/beal.html Peter told me he often gets candidate solutions that the sender hasn't even validated.

schoen 7y ago

I used to answer correspondence for the EFF Cooperative Computing Awards (which are an actual financial prize for finding very large primes) and people who wrote in were almost uniformly either kids or people meeting all of the criteria mentioned here. Almost none of them thought it was important to understand any prior results about primality testing before submitting a claim for the prize, while a majority didn't seem comfortable with the idea of a mathematical proof or theorem. In general, they didn't have a sense that some properties are always true, some are never true, and some are sometimes true and sometimes not true, and that mathematical reasoning can often definitively establish which of these categories a particular property is in.

secraetomani 7y ago

> In fact, members of the academy were so tired of being inundated with quackery that in 1775 they passed a resolution not to accept solutions to the problems of circle squaring, angle trisection, or cube doubling. This is hilarious.

vector_spaces 7y ago

While many people who become preoccupied with "problems" like these are operating in bad-faith and can't be swayed otherwise, I would be very surprised if a large number of them (if not most of them) weren't just lay people who were simply curious, who had poor experiences learning math or technical subjects growing up, and for once read about some mathematical "problem" that was accessible to them, were excited by it, and set about exploring it not realizing it was actually a red herring. And unfortunately, if you lack a good foundation, you won't be able to realize the "problem" you're working on is actually a red-herring, and the rabbit holes you wander through when researching these "problems" will just teach you further bad habits and crankery. For the sake of those people, I don't think it's fair or right to immediately assume bad faith and take the attitude of "run for the hills" when met with anyone who's gone down such a path. And I don't think it's right to make a mockery of them either (except of course for the ones that start trying to write books, teach seminars, or submit papers about their "discoveries" without ever getting it right). Instead maybe we can point them towards resources so they can fix their faulty foundation and find more productive ones? No need to engage them further. Just give them something -- even something canned -- to sate the obvious curiosity that they have and give them a little direction. At the very least we can not mock them and assume bad faith -- there's nothing wrong with being curious.

rabidrat 7y ago
A "crank" is a very specific type of person, who will not heed any constructive criticism and in fact deliberately avoids resources from the establishment. Any dismissal is viewed as a conspiracy by the establishment to keep their brilliant ideas from dismantling the establishment's sacred cows. Like concern trolls, their goal is seemingly to waste the time and energy of anyone willing to listen or engage, except they're not doing it wittingly, so you just wind up feeling like a jerk when you inevitably have to ignore their latest 20-page ramble and get some real work done.
knzhou 7y ago
As they say, sounds good, doesn't work. You can tell the genuinely curious sort from true cranks at a glance, and this article is about the latter. Every academic has interacted with far too many true cranks. I always try to give rebuttals that are accessible, explaining in plain English what is going wrong and giving resources for follow-up learning. It doesn't work -- you get "that's cute, you still believe in textbooks, when I've proven them all wrong."

rdc12 7y ago

I wonder if Andrew Wiles had taken a different approach when announcing he had solved Fermat's Last Theorem if he would have been considered a crank. I would imagine that problem would have attracted nonsense solutions prior.

anyfoo 7y ago
That's a big hypothetical, though. Andrew Wiles had been producing sensible mathematics in the community already, so there was no reason to suspect him of being a crank. Also, his proof did not emerge in a vacuum, he pursued approaches that were already known to be connected to FLT. As for FLT attracting nonsense solutions: Yes, plenty of them. It being such a simply stated problem, and immediately understandable to laypeople certainly exacerbated the problem.
- rdc12 7y ago
  Fair point I have no familiarity with his earlier work, or even that there was suspicion of a connection, I did mean for my point to be a bit more general, just seemed like a reasonable example

thecopyeditor 7y ago

A long time ago, I spent the summer at my university where I was a mathematics major. I needed a job to pay for groceries, so I took a part time copy editing job at the math journal. We got at least one "whack job" paper a week. Bear in mind this was when the internet was first getting traction, so I knew some of these guys from usenet… lol

Semiapies 7y ago

See also this site on weekends, when every "physics revolution" and "fix" for dark matter in cosmology gets posted.about. A rare genuinely obligatory xkcd: https://xkcd.com/1758 https://xkcd.com/1758

breck 7y ago

"Beware of Cranks" shows a terrible understanding of how major progress in science and technology happens. If you go around flipping the "crank bit", sure, you will save yourself spending time evaluating lots of correct negatives and have more time to make on incremental progress, but you will also have a couple of false negatives, one or two of which will go on to change the world. World change is dominated by black swans. Conversely, Thiel's Hereticon conference idea is brilliant and shows a terrific understanding of how progress in science happens.

dang 7y ago

A previous discussion of Underwood Dudley's classic article: https://news.ycombinator.com/item?id=14446708 https://news.ycombinator.com/item?id=14446708