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A liar who always lies says "All my hats are green."

theguardian.com

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Re: A liar who always lies says "All my hats are green."

#201

Post by dleeftink »

Retric wrote: post #162
dleeftink wrote: post #141

Earlier quoted context omitted.

Why not hopefully more? Less? Is mathematics this inaccessible to the other 99.9%?

Another way of considering that statement is diminishing returns on the utility of mathematicians. Some is good, but more isn’t necessarily better.

And less isn't necessarily better either. But as we further mathematics, large cohorts are falling behind.

I welcome puzzles, but I also think we need to shed some of the exclusionary aspects of mathematics/compsci, the brunt of which are far too known: inaccesible formalisms, leetcode, competitive grants/hackathons, steep admission requirements, code bounties, interview puzzle rounds, etc.

Some necessary and organised in good faith I'm sure, but I hope we can move past the implicit assumption that 'maths/code isn't for everyone' and self-select based on that, as that doesn't further the cause.

Re: A liar who always lies says "All my hats are green."

#202

Post by hinkley »

mjburgess wrote: post #146
sillysaurusx wrote: post #142

Earlier quoted context omitted.

It’s not so much that an inability to solve them means you’re deficient, as it is that an ability to solve them means you’re capable in ways most people aren’t. My wife is great at puzzles, and it’s always humbling to watch her sail through them. I agree that puzzles alone shouldn’t e.g. determine whether you’re a good fit for a job, though. That’s one of the more annoying parts of software interviewing.

I think it should be the duty of the person asking the question to find a isomorphism to another question that the majority of people can answer. Eg., rather than asking about the risks of A,,B,C given various probabilities etc. ask them to make bets in a highly familiar environment with a resource that has uniform marginal utility to them... so eg., "suppose you were at home and your friend does..., how much of your…

> The problem that most people are solving is: "what do i say to make this person/question go away" reply

This is it.

Never attribute to incompetence that which can be readily attributed to apathy.

Re: A liar who always lies says "All my hats are green."

#203

Post by mjburgess »

Suppafly wrote: post #188
mjburgess wrote: post #116

Earlier quoted context omitted.

This is generally the case for the vast majority of puzzles, and it equally drives me mad in those areas where academics set "puzzles" and conclude that people's inabilty to "solve" them is some cognitive deficiency. I've rarely encountered a case where it is isnt an extreme lack of self-awareness in the questioner -- eg., being extremely overfit to language/notation/etc. localised to their own area of expertise.

>and it equally drives me mad in those areas where academics set "puzzles" and conclude that people's inabilty to "solve" them is some cognitive deficiency. Does that actually happen in academia? It seems to mostly be a social media thing.

So frequently I'd say its the main case. Researchers are extremely poor at controlling for competing explanations, in many cases, strongly incentivsed not to.

Suppose you're writing a paper what do you write: option A) Average People Cannot Understand Probaility!?!?!, option B) Inexperienced test takers with unfamiliar notation fail to grasp meaning of a novel question; option C) survey participants on technical questions often do not adopt a literal interpretation of question; D) etc. etc.

In general researchers are extremely loath to, or poor at, recognising there's 101 alternative explanations for any research result using human participants and 99.99% of the time just publish the paper that says the experiment evidences their preferred conclusion.

Re: A liar who always lies says "All my hats are green."

#204

Post by LudwigNagasena »

Supermancho wrote: post #183
LudwigNagasena wrote: post #177

Earlier quoted context omitted.

Would you agree with the following proposition: “if all of my unicorns fly, then some of my unicorns fly”?

Yes

So if “all my hats” doesn’t imply that I have at least one hat, “some of my hats” doesn’t imply it either; otherwise we wouldn’t be able to derive “some” from “all”.

Hence, “some of my hats are green” doesn’t imply that “at least one of my hats is green”. That’s a claim that contradicts both traditional formal logic interpretation and common sense English interpretation.

Re: A liar who always lies says "All my hats are green."

#205

Post by fargle »

gryn wrote: post #163
rawgabbit wrote: post #103

I never liked this type of puzzle. It is not formal logic but more about the idiosyncrasies and conventions of the English language. I put this puzzle on par with Agatha Christie’s murder mysteries. It requires a suspension of disbelief and logic to be believable. Someone who always lies means in the purest sense means you cannot trust anything they say. Even the word “hat” could mean they are talking about their pet…

yeah, you can add most "paradoxes" to that list. the one I hate the most is the Monty Hall Problem.

monty hall is not a true paradox. it could be classed as "veridical" (truthful) paradox, or i've seen it called a pseudo-paradox.

but you realize that it's unambiguously mathematically true without gimicky word-play or puns or other logic puzzle trickery.

it's just simply an un-intuitive result. most statistics really is.

curious: why the hate for the monty-hall problem?

Re: A liar who always lies says "All my hats are green."

#206

Post by SirMaster »

paxys wrote: post #121
rawgabbit wrote: post #103

I never liked this type of puzzle. It is not formal logic but more about the idiosyncrasies and conventions of the English language. I put this puzzle on par with Agatha Christie’s murder mysteries. It requires a suspension of disbelief and logic to be believable. Someone who always lies means in the purest sense means you cannot trust anything they say. Even the word “hat” could mean they are talking about their pet…

These puzzles are entirely formal logic. Now you may not like or understand the intricacies of the logic/math and how it interacts with the English language, but the rules, and thus the solutions, are pretty objective and not open to interpretation.

Then the puzzle shouldn't use the word lie, because to lie can mean to be deceptive, and saying all your hats are green when you have no hats is clearly deceptive and thus can be considered a lie.

Re: A liar who always lies says "All my hats are green."

#207

Post by scoofy »

tantalor wrote: post #175
dwheeler wrote: post #145

One complication is that in typical English, if you say "All my hats....", you are simultaneously making an existence statement that you have at least one hat... but the usual formal logic "forall" quantifier does NOT presume existence. Here's a formal proof that "forall" has a "surprise" meaning for those not well-versed in formal logic: https://us.metamath.org/mpeuni/alimp-surprise.html I propose that when translat…

> in typical English you are making an existence statement No, you're not.

Oh boy... so I actually wrote a thesis in graduate school on conversational implicature, Paul Grice, and various other theories of implying things.

I would actually agree user dwheeler here.

Whether or not you agree with Gricean implicature theory (I do not), the point is that making a claim about a group that doesn't exist is absurd. Absurd statements do not convey meaning, and language is a tool for communication, thus it is generally an assumed axiom that statements will have meaning. Here, even when people make borderline nonsensical statements, we assume there is a metaphor or language game involved.

So, by making a statement about 'all my hats', if the number of hats you have is zero, then any predication is absurd and the statement is absurd, so given an axiom of not making absurd statements for natural language, you can assume there are at least two hats. Obviously there are no formal rules here, but the functionality of natural language demonstrates that these heuristics exist.

https://plato.stanford.edu/entries/implicature/

Re: A liar who always lies says "All my hats are green."

#208

Post by SilasX »

gpderetta wrote: post #168
GuB-42 wrote: post #150

Earlier quoted context omitted.

That's the reason natural languages are not very well suited to formal logic, and one of the reasons programmers use programming languages. If we reframe it using C++ "std::all_of" function over an array of strings called "hats", and say that the following must be false (because he is a liar): std::all_of(hats.begin(), hats.end(), [](std::string hat) { return hat == "green"; }) Then we can answer the questions withou…

The question becomes why all_of returns true for an empty list. A better example would use std::accumulate and an 'and' function argument. The original STL documentation [1] described the function argument as having to model the Monoid[2] concept and have an identity value. The identity value for the 'and' Monoid is 'true'. [1] https://www.boost.org/sgi/stl/MonoidOperation.html [2] note: Monoid, not Monad, and yes, c…

>The question becomes why all_of returns true for an empty list.

Yes! Before it became a programming problem, I considered the implications of this decision for common speech. In that case, it will generally be expected that when someone says "all my hats are green", they have at least one hat, probably because otherwise it doesn't hit the relevance threshold to make such a statement worth saying.[1]

Based on this, with my younger, hornier mind, I would joke that, "I have gone on a date with every female cheerleader at my university." (All the cheerleaders at my university are male.)

The idea being, an equally valid convention would be to read the statement as "there exists no element violating all the predicates" i.e. no one who is both a "female cheerleader at my university" and "someone I have not gone on a date with".

And this convention, it turns out, is what C's all_of (and Python's all()) uses.

But I'd still balk at someone using that trick in common speech -- it's at least an attempt to be misleading.

[1] See the "Maxim of Relevance": https://en.wikipedia.org/w/index.php?title=Cooperative_princ...

Re: A liar who always lies says "All my hats are green."

#209

Post by hinkley »

ninalanyon wrote: post #190
bingohbangoh wrote: post #154

Earlier quoted context omitted.

I agree. It reminds me of the math "puzzles" on Twitter which go: 1 shoe + 1 shoe = 2 2 shoes + 2 shoes = 4 3 shoes + 2 shoes = ??? And the answer isn't 5 because a) we're not counting shoes and b) the shoe laces were different colors. There's nothing clever, it just teaches you to be hyper cynical and question every little detail which isn't relevant to either Math or the real world.

I have a little monograph written many decades ago on Dimensional Analysis. Since reading it, not quite so many decades ago, I simply dismiss puzzles of this sort because the two sides of the equations are dimensionally incongruent. This means that I have to try to guess the state of mind of the questioner rather than solve a logic problem. It's a handy stance because I'm no good at either solving logic problems or g…

I expect people in different branches of statistics or physics would potentially come up with different answers based on what sorts of series appear in their realm of expertise.
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