Beware of Cranks: Misguided attempts to solve impossible mathematical problems • Hacker News Board

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

#11

Post by nikanj » Wed, Oct 09, 2019, 10:01 PM UTC

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.

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

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

#12

Post by throwaway2048 » Wed, Oct 09, 2019, 10:04 PM UTC

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.

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

#13

Post by throwaway2048 » Wed, Oct 09, 2019, 10:05 PM UTC

paultopia wrote: post #5

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?

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.

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

#14

Post by te_platt » Wed, Oct 09, 2019, 10:21 PM UTC

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.

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

#15

Post by ahelwer » Wed, Oct 09, 2019, 10:22 PM UTC

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 actually mathematically impossible. Even the halting problem is easily solved in practice.

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

#16

Post by xyzzyz » Wed, Oct 09, 2019, 10:39 PM UTC

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…

> I'm against cryptographic backdoors, but claiming they're not technically possible is a losing position.

I never seen anyone serious ever claim that cryptographic backdoors are impossible.

> Even the halting problem is easily solved in practice.

Like, how exactly?

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

#17

Post by xyzzyz » Wed, Oct 09, 2019, 10:41 PM UTC

throwaway2048 wrote: post #13

paultopia wrote: post #5

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?

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.

Yes. The better way to phrase it would be that some angles are impossible to construct, and importantly that includes a trisection of some angles that can in fact be constructed.

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

#18

Post by ahelwer » Wed, Oct 09, 2019, 10:43 PM UTC

xyzzyz wrote: post #16

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…

> I'm against cryptographic backdoors, but claiming they're not technically possible is a losing position. I never seen anyone serious ever claim that cryptographic backdoors are impossible. > Even the halting problem is easily solved in practice. Like, how exactly?

If you're writing business logic in a modern programming language your code can almost certainly be proven to halt. Very few people are running around coding up the Collatz conjecture or feeding programs as input to themselves.

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

#19

Post by xyzzyz » Wed, Oct 09, 2019, 10:49 PM UTC

ahelwer wrote: post #18

xyzzyz wrote: post #16

Earlier quoted context omitted.

> I'm against cryptographic backdoors, but claiming they're not technically possible is a losing position. I never seen anyone serious ever claim that cryptographic backdoors are impossible. > Even the halting problem is easily solved in practice. Like, how exactly?

If you're writing business logic in a modern programming language your code can almost certainly be proven to halt. Very few people are running around coding up the Collatz conjecture or feeding programs as input to themselves.

It's clearly not true in any practical way. because most programs these days are huge beasts depending on stacks of millions of lines of code, so little can be conclusively proven about those. It's also wrong in theoretical sense, because what you're talking about is not "halting problem" at all.

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

#20

Post by incompatible » Wed, Oct 09, 2019, 10:52 PM UTC

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…

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.