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Beware of Cranks: Misguided attempts to solve impossible mathematical problems

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

#51

Post by knzhou »

sopooneo wrote: post #41
throwaway2048 wrote: post #12

Earlier quoted context omitted.

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 i…

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...

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

#52

Post by knzhou »

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…

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."

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

#53

Post by copperx »

nikanj wrote: post #11
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…

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.

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

#54

Post by copperx »

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.

Sure, you can do that with formal methods, but proving that a program is correct or that it halts is not the same as solving the halting problem.

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

#55

Post by UncleMeat »

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.

The entire field of static analysis is "solving" undecidable problems effectively and productively all the time. Just accept a few false positives or false negatives and suddenly the field opens up to be amazingly useful.

Yes it isn't literally solving the halting problem. But I've had a weird number of people tell me that the stuff I work on doesn't work because of things they learned in undergrad.

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

#56

Post by gluelogic »

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.

This comment is not germane to the point you were making, just wanted to share:

I am a web dev who knows nothing of the Collatz conjecture, so I had to check out the Wikipedia article for it. Thanks for teaching me something today.

I wrote this JavaScript function based on what I read in the article. It's a simple algorithm but it was fun to see it work. For anyone who is in my shoes (weak mathematical background), running this function might be a useful supplement for illustrating the gist concept of the Collatz conjecture:

    function collatz(i) {
      console.log(i); // for visual feedback
      if (i

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

#57

Post by nikanj »

copperx wrote: post #53
nikanj wrote: post #11

Earlier quoted context omitted.

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…

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.

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.."

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

#58

Post by YeGoblynQueenne »

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…

Thank you for a comment coming from a position of genuine compassion for people who may not have had many opportunities in their life to train their minds.

The description of cranks as old, retired males with a minimal mathematical background given by U. Dudley seems to agree with what you say, btw.

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

#59

Post by YeGoblynQueenne »

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?

That's not what the OP means, from what I can tell, but in the real world even a program like "while true {}" can be guaranteed to halt because eventually someone will figure out it's stuck in an infinite loop and abort it.

(tongue in cheek, of course, but I think the OP is trying to capture a similar pragmatic view of the halting problem)

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

#60

Post by YeGoblynQueenne »

BeetleB wrote: post #35
xyzzyz wrote: post #19

Earlier quoted context omitted.

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.

Can't speak for ahelwer, but once at work we had to show (for certification purposes), that our program wouldn't get lost in an infinite loop. Now from a realistic standpoint, all they wanted was some evidence we had considered this possibility and some data/argument to show our confidence that it wouldn't. This was a simple program - you could confirm the algorithm wouldn't run forever by examining the code - look a…

In a company I worked for, systems were brought to their knees because of a while loop that went infinite under poorly tested conditions. There was a meeting and the head of the dev team came down to tell us that, in the meeting, it was decided that we should not use iteration any more because it runs the risk of going infinite. Instead, we should use recursion for all our looping needs.

That was in a C# shop so of course the "decision" was never implemented. My guess is that this was a completely mad decision taken by non-technical managers in a moment of panic, who had pressed our tech lead a bit too much on why software breaks and what can be done to avoid it breaking- and then latched on to some off-hand comment about recursion being an alternative to iteration, and ran with it.

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