
Beware of Cranks: Misguided attempts to solve impossible mathematical problems - Hooke
https://www.laphamsquarterly.org/roundtable/beware-cranks
======
vector_spaces
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
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
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
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.

~~~
sopooneo
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
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...

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te_platt
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.

------
hprotagonist
> 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.

~~~
nikanj
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

~~~
copperx
Well, MOSH breaks through the speed of light latency limitation of SSH by ...
predicting the server's response.

Although the laws of physics can't be broken, in certain scenarios we can
simulate we have done just that. And often that's just what you need to get
ahead of your competition.

~~~
nikanj
You sound just like a VC!

"You're saying we can't do HFT between Tokyo and New York faster than the
speed of light? Here's a completely unrelated product, that does something
completely different, and the limit they're working with doesn't really apply
to us. So it is possible! Maybe you should go to Burning Man, that would open
your mind.."

------
dekhn
[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.

------
Animats
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.

------
schoen
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.

------
breck
"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.

------
rdc12
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
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
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

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paultopia
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?

~~~
recursive
"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
Oooh. I was imagining a compass like you're given in school, with labels on
it, and ditto a ruler. :-)

~~~
SamReidHughes
That would be a protractor, which would be allowed if there were 340 degrees
in a circle.

------
dang
A previous discussion of Underwood Dudley's classic article:
[https://news.ycombinator.com/item?id=14446708](https://news.ycombinator.com/item?id=14446708)

------
Semiapies
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)

------
thecopyeditor
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

------
secraetomani
> _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.

