Comment by schoen | Hacker News Reader

Comment by schoen | Hacker News Reader

I get the e-mail for the EFF Cooperative Computing Awards

https://www.eff.org/awards/coop

so, despite having put lots of effort into not having people make spurious claims, I hear from a whole lot of math cranks.

Two things that I find striking are many people's level of confidence that they can personally "solve the problem" (in this case, by inventing some kind of "formula for primes" that has eluded the organized mathematics world for decades), and many people's lack of understanding of what a solution would consist of (in terms of knowing that mathematical proofs exist, and being able to understand whether they have a theorem or just a conjecture).

Our situation is especially tricky because we chose a problem that experts said would require lots of computational resources and couldn't be solved by new mathematical insight, but then we didn't outright forbid people from trying to solve it by insight. So a lot of people see an exciting challenge, like "they think it will take a lot of computer time, but if I can just see the pattern, I can skip all of that!". Also, we have a large monetary reward for solutions and so people are excited by the idea that they have them and are about to receive a bunch of money.

I think it's true that many of the people who contact me about this are excited about mathematics in the way that people who contacted Dr. Hossenfelder were excited about physics (and, as pdkl95 said, that Carl Sagan's cab driver was excited about science). But it's still frustrating that, after we've gone to some lengths to say that you need a proof and not just a guess, and that decades of research indicate that you can't find primes of this size without significant computer time, people are still so confident that their guesses are right and so resistant to accepting that they haven't met the awards criteria.

It would be interesting to see an equivalent service for talking to mathematicians and to see what some of the people who contact us might get out of it, and whether it might inspire them to pursue more constructive things. (I always wish that our awards would motivate someone to start doing Project Euler problems or something...) If someone set up that "talk to a mathematician" service, I would probably try to send lots of people their way.

This raises the meta-question of how best to run filters for possibly-interesting-but-expensive-to-assess claims, posts, and traffic.

One model I've heard of is to put the cranks in contact with each other, which at least offloads the problem. I'm not sure it's an effective filtering mechanism, however.

This is related to the general problem of innovation (in maths or otherwise), in which the view that inventors simply toss ideas out at random but the good inventors are far better at sussing out the good ideas and rejecting bad ones may hold some validity. See J. Doyne Farmer, John Muth (whom Farmer cites: John F. Muth, (1986) Search Theory and the Manufacturing Progress Function. Management Science 32(8):948-962. http:// dx.doi.org/10.1287/mnsc.32.8.948), John Holland, etc.

There are implications for online collaborative filtering, both in general discussions (e.g., HN) and academic publishing (e.g., PLOS ONE).

> put the cranks in contact with each other

Three Cranks of Ypsilanti, so to speak?

Not familiar with the reference. I think Feynman may have used this technique though.

More seriously, I was hoping you'd pick up on the overarching theme: is there an effective way to sort through the autodidact chaff to find wheat?

My own area of crankdom is economic theory. I have (and I believe this earns me John Baez crank points) studied the topic in school, and am doing a boatload of research on both current state and history of theory and the dynamics of its spread. Interesting stuff. I'm actively trying to shut the fuck up for the most part, other than 1) noting what I'm currently pursuing, 2) questions of interest, 3) references of interest (e.g., the Santa Fe Institute mafia generally, mentioned above), and 4). occasionally contacting specific academics with specific questions, usually about some element of theory, historical item, etc., rather than a full-fledged Theory of Everything. Then withdraw for further mulling. I'm batting about 50-50 on responses, some quite helpful.

But it does put to mind the question of how one ought approach questions quite fundamental to the nature of a large field of study and/or propaganda (economics is ... curious in many regards).

https://en.wikipedia.org/wiki/The_Three_Christs_of_Ypsilanti

To your point, I was talking to someone about the idea of evaluating proposed proofs (like for the awards I was talking about) by requiring them to be submitted in a formal proof system. Apparently even for large computations there can be ways to submit spot-checkable logs or summaries of the computation, kind of like zero-knowledge proofs, where you can randomly pick locations in the log and confirm that it's internally consistent, even without repeating the entire computation.

I don't think any of these techniques will help for anything outside of mathematics or computational projects, though!

I've been kicking around a few thoughts over the past few decades.

There's a fundamental limit to the number of distinct messages a person can assimilate in a day. I've noticed from several reports of personal email patterns (Wolfram and others), that about 300/day is a typical upper bound. That's 1.6 minutes per email (or an email every 1.6 minutes) in an 8 hour day, though it's not atypical to see patterns where someone dedicates a few hours of the day to managing emails.

I ran across a truly staggering statistic of the rise in the number of communications a manager received per year from 1970 to 2015. On the order of ~400 (per year) to 30,000. I suspect some possible undercounting (phone and direct in-person messages, as well as, say, message slips may have been omitted from the earlier tally), but that's a change from ~2 messages per day to about 120. The time and consideration given each has to fall.

I've spent quite some time pondering collaborative filtering systems. Typically, these strive to rate and rank, and sort by significance individual messages. On a typical Web or online service, all visitors will see all messages, eventually. This can produce problems when, say, a top-ranked subreddit has several thousand comments in it -- it's unreasonable to expect anyone to read them all, but also somewhat unfair to those who contribute later to be fated to not be seen at all.

The HN front page and new submissions pages suffer a somewhat similar problem.

One model might be to target a given page or platform for a set number of visible submissions at any one time, but using the content filtering system to adjust not the position on a page, but the probability that any given user would see the content.

An alternative might be to divide content into several categories, a logarithmic progression of quality. I'm fond of Likert scales, usually 5-9 levels. Here, the idea is that each level is an order of magnitude "better" (I'll explain the quotes) than the previous, with increasing likelihood to be seen. All content should be seen by someone. Better content is seen by more people. With a five level scale, L-1 content is seen by 1:10,000 visitors, L-2 by 1:1,000, L-3 by 1:100, L-2 by 1:10, and L-1 by 1:1. It might well be possible to work with smaller numbers of categories.

Another advantage is that this system would tend to reduce the filtering overhead as content was more highly rated, such that more trusted / discriminating raters could be explicitly called in to assess the small number of highly-ranked posts. The slush pile, as it were, is fanned out among many, the good content filters toward the top, where it's multi-checked for quality (I'm assuming here that the objective is quality and not just "attracts eyeballs"), including being flaggable for various negative characteristics (misleading, spam, social norms violations, low-effort posts, etc.).

There's also the challenge that explicit content rating tends to be problematic -- there are a few too many incentives to game any rating system, and much behavioral indication of quality or interest which isn't explicit.

In the cranks'n'geniuses model, you'd divvy up your recipient pool such that incoming submissions get farmed out and no one evaluator has to see too many of them, but all submissions have at least a reasonable likelihood of being reviewed. Better submissions go up the set (perhaps subject to specific tests, e.g., can someone find an example which contradicts the claim). And expert's time wastage is minimised.

And whether or not the submitters think they themselves are Jesus and/or the others dead beings manipulated by experimenters largely doesn't matter.

With a five level scale, L-1 content is seen by 1:10,000 visitors, L-2 by 1:1,000, L-3 by 1:100, L-2 by 1:10, and L-1 by 1:1.

I'm lost. Does the repetition of L-1 and L-2 for two different values have a meaning that I haven't figured out yet, or are these typos?

I have no idea how that happened.

Should have been L-1, L-2, L-3, and L-4. Presumably an L-5 given I started off talking about 5-point scales.

Log10 might be a bit much. Log2 or log-e might well be more appropriate, or other scaling factors.

Memo to self: no HN commenting when brainfarting.

Oh god. "Formula for primes" - I was involved in a way too long forum discussion where everyone involved was trying to convince the guy putting forth his idea for generating primes that he was merely going round in circles, proving and reproving identities.

As a former physicist, I think that math is way harder to talk about to laypeople, though there can be a wide variation in difficulty by subfield. Maybe number theory can be accessible, but analysis, say, would be pretty opaque. Not to mention some of the more exotic branches of math.

I've unfortunately received somewhere around 100 supposed formulas for primes in the past decade and a half. :-(

There's a great Wikipedia article about this:

https://en.wikipedia.org/wiki/Formula_for_primes

But most of what people send me is along the lines of "numbers containing only odd digits, that don't end in 5" or "4k+1 for any k, if it contains only odd digits", or "(p-1)²+7 for any prime p" or whatever. A kind of unfortunate example was an elementary school girl who became convinced that numbers containing only odd digits are always prime (many people are tempted by some form of this idea), and spent several weeks writing such digits down in a composition notebook in order to form an integer that would be big enough to qualify for one of our awards.

And the counterexample of 15 didn't work?

Or 9.

Ah. I took "digits" to mean "must be plural", not "could be".

I've come up with counterexamples for every such formula or rule that people have sent me (usually running a Python loop with gmpy2.is_prime() or something), but unfortunately the existence of the counterexamples somehow didn't occur to them before they wrote in in the first place.

https://en.wikipedia.org/wiki/Mathematical_coincidence is a big problem because people will sometimes conjecture a pattern and then find that it holds for 6 or 7 integers and conclude that it's right. Or if they find a counterexample, they might just make a minimal modification to the conjecture and conclude that they're fixed it! So there are lots of these that will say "unless the number is..." and presumably give some other random property that the counterexample that the claimant found had.

It feels like some people think that mathematics works by people guessing rules and then checking them, and regarding the rules as right if they "check out" in practice. (I know that there's been lots of progress made from guesses and conjectures and numerical experiments; the issue is just what comes after the guess!)

> mathematics works by people guessing rules and then checking them

This will sound facetious, but I suspect many people treat great swathes of life this way. My wife has a friend who tries any random googled herb-based cure any time she gets ill. Recovery from this illness, this cold or flu, is always taken as proof of the validity of the cure, regardless of how long she's had to ingest it.

You, reading this, have already thought of half a dozen ways to disprove her cures, as have I, however no amount of evidence can assuage this need to believe. At this point my theory is that this belief forms an intractable part of her personal identity.

At the core of all of this, and perhaps for these "autodidact physicists" as well, seems to be a very primal need to understand the universe in terms comprehendible one's self, regardless the cost.

> mathematics works by people guessing rules and then checking them

This will sound facetious, but I suspect many people treat great swathes of life this way

Including programming. Good programmers are the ones who try to derive the underlying rules, instead of trying something and checking if it works for a couple cases.

I don't know if we're talking about the same guy and the same forum, but I remember a very similar story on a forum I used to frequent. The guy also had a plan for interplanetary spacecraft propulsion, that involved a weight moving to the back of the craft, being thrown towards the front of the craft where it's caught, and repeating the cycle.

The theory in his mind depended on there being a difference between the weight being 'thrown' and merely being 'moved and released' towards the front of the craft. It took a few patient techies, one of whom was a professional physicist, quite a while to explain that there was no physical difference between 'throw' and 'release'.

Nice bloke, but a classic example of 'not being able to talk the talk', as discussed in the article.

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