Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Beware of Cranks: Misguided attempts to solve impossible mathematical problems

laphamsquarterly.org

Post reply on HN
Print view View original

41–50 of 63 posts

Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems

#41

Post by sopooneo »

throwaway2048 wrote: post #12
knzhou wrote: post #2

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…

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.

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.

Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems

#42

Post by 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

Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems

#43

Post by mcqueenjordan »

ahelwer wrote: post #15
hprotagonist wrote: post #3

> 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.

There's a flipside of this, where people incorrectly lord "mathematical impossibility" over others as a way to shut down discussion. You see this on the topic of cryptographic backdoors especially. I'm against cryptographic backdoors, but claiming they're not technically possible is a losing position. The interface between plain language and math is messy. I don't think I've ever seen something suggested that was act…

> Even the halting problem is easily solved in practice.

You don't grok what the halting problem is. What you're describing (I assume) is determining if a specific program is going to terminate. That's not the same problem.

From Wikipedia:

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist.

Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems

#44

Post by anyfoo »

rdc12 wrote: post #39

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.

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.

Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems

#46

Post by rabidrat »

vector_spaces wrote: post #36

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 i…

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.

Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems

#47

Post by 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.

Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems

#48

Post by ahelwer »

mcqueenjordan wrote: post #43
ahelwer wrote: post #15

Earlier quoted context omitted.

There's a flipside of this, where people incorrectly lord "mathematical impossibility" over others as a way to shut down discussion. You see this on the topic of cryptographic backdoors especially. I'm against cryptographic backdoors, but claiming they're not technically possible is a losing position. The interface between plain language and math is messy. I don't think I've ever seen something suggested that was act…

> Even the halting problem is easily solved in practice. You don't grok what the halting problem is. What you're describing (I assume) is determining if a specific program is going to terminate. That's not the same problem. From Wikipedia: Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist.

I "grok" very well what the halting problem is, thank you. It's colloquially used in the sense of being unable to tell whether a program terminates. For reference I direct you to early static analysis tool promo materials (ex. Coverity) which usually explicitly address the "doesn't this run into the halting problem?" question given its common occurrence.

Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems

#50

Post by rdc12 »

anyfoo wrote: post #44
rdc12 wrote: post #39

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.

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…

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
Post reply on HN