A seemingly intractable problem

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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 7:38 pm 

Lomax » December 18th, 2016, 8:35 am wrote:
NoShips » December 18th, 2016, 12:31 am wrote:Erm, I've been a little preoccupied, L. Almost went mad over these dang triangles. LOL.

Haha. Well I'll let you in on another reason why the quiz is cruel: Q2 is underdetermined too, as far as I can tell. It's not possible to just simplify the equations given what you (reasonably) know, and then solve them together. I had to try a few ex hypothesi possible values for the shapes in equation five, and plug them into equation 1 to see if they worked. Which meant making assumptions about what the big triangle might mean, too. So there's guesswork at all steps. But the answer - when you get it - kind of seems simple and beautiful enough that you figure it must be the one they were after.


Ah, you raise a wonderful point, one that I considered posting on earlier. Was your solution due to following a "Method"" -- i.e., did you derive a solution from the data? -- or inspiration -- i.e., did you bring a hypothesis to the data?

If there was a "method", I'd be wallowing in Nobel prizes too.

P.S. Just got another book on Quine from the library. We must run a thread on him. Or has that been done?

Are you aware of Searle's putative refutation of his "indeterminacy of translation" thesis? Quine can be a bit scary, I think, insofar as he celebrates an apparently absurd result as a "discovery". Searle sees it as an absurd result simplicter. Tee hee.
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 7:46 pm 

Well take everything I say with a pinch of salt, because my maths head isn't what it used to be, and Natural ChemE is overwhelmingly better at such things. But I hypothesised:

1. Adjacent shapes are added together (ie. "square, square" means "square plus square")
2. Containing shapes represent functions of contained shapes (ie. "big triangle with little square in it" means f(x), where (x) is little square, and big triangle is f)
3. The three different shapes in equation five have values a,b,c, which I won't tell you because that might give away the whole thing for some people.

There's other hypothetical work later - to abduce the function represented by the big diamond, you only have three terms of the sequence. But that sort of thing isn't unique to this test - nearly every IQ test I've taken, maths A-levels, the "Maths Challenge" and "European Kangaroo" competitions, all ask the same kind of question. "What's the next term in the sequence?" There's the reasonable answer, and the maybe infinite set of possible answers. We go with the simplest-expressible function.
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 7:49 pm 

Hmm, think I'll stick to journalism. Erm, available for an interview? If not, how about a centrefold for the ladies?
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 7:50 pm 

Well I'm sorry to say that journalists are left with all the same problems ;)
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Re: A seemingly intractable problem

Postby Natural ChemE on December 17th, 2016, 7:59 pm 

Lomax » December 17th, 2016, 6:23 pm wrote:I'm curious ChemE. Are you basing this on the nature of the quiz (for instance, the fact that question 6 is underdetermined) or is there something you know about its creators?

The considerations that went into that quiz, from its conception to its implementation, are badly flawed. I suspect that that quiz would tend to mislead those who invest time in it.

The site lists two creators. The second's still living, so I'm constrained in what I can say about him. But the first one committed suicide last year at age 40. This more narrative article tries to explain what was going on with the guy, though in reality he was just really mentally ill.

That alleged IQ quiz is nothing of the sort, and the intro section of that webpage is fairly toxic. People who embrace that world view are likely to suffer as its author had. So, while puzzles can be fun, I guess I'm just concerned that that guy's diseased mental state might infect others through his words; the little, subtle breaks in logic are enough to lead someone in a bad direction.
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 8:30 pm 

Natural ChemE » December 18th, 2016, 12:59 am wrote:That alleged IQ quiz is nothing of the sort, and the intro section of that webpage is fairly toxic. People who embrace that world view are likely to suffer as its author had.

What world view?

Natural ChemE » December 18th, 2016, 12:59 am wrote:So, while puzzles can be fun, I guess I'm just concerned that that guy's diseased mental state might infect others through his words; the little, subtle breaks in logic are enough to lead someone in a bad direction.

Fair enough. Q16 seems too easy to be alongside the other questions, which does make me wonder whether there are just trick questions. Are we supposed to assume that simultaneous plane cuts cannot intersect? Either way the question is easy, but only once we know that bit, and it isn't stated.
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Re: A seemingly intractable problem

Postby Braininvat on December 17th, 2016, 10:00 pm 

Took 15 minutes, seem to be getting there. Seems like operations are simple arithmetic stuff and big shapes simple fumctions. So far no urge to violate Colorado historical zoning ordinances and become a misanthrope, so I guess I've ducked the memetic boobytraps.

Sorry, that was a bit dark, and I am sorry the fellow shot himself. I've known smart guys who do something called "robotripping," which is a way of coping with the isolating aspects of high intelligence by lowering theirs. Some use exotic substance blends (cough syrup and vodka), some use television, e.g. David Foster Wallace who claimed to be a terrible tv addict. Wallace also killed himself around age 40. Ok, I've dispensed enough good cheer!
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Re: A seemingly intractable problem

Postby Braininvat on December 17th, 2016, 10:02 pm 

For relaxation, I recommend the Daily Problem at chess.com. it's usually fairly easy and you feel smarter when you're done.
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 10:03 pm 

LOL!!!

Got any deceptively difficult questions that only imbeciles can answer?
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Re: A seemingly intractable problem

Postby Braininvat on December 17th, 2016, 10:09 pm 

Why would you want a question like that?

(That was the question)

Seriously....

"Why was 6 afraid of 7?"
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 10:10 pm 

Hmm, tougher than I expected. Let me consult my almanac.
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Re: A seemingly intractable problem

Postby Braininvat on December 17th, 2016, 10:12 pm 

Edited too late.

Why was 6 afraid of 7?
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 10:14 pm 

Coz Lomax eight her
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 10:14 pm 

Yes, preparing my speech already
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 10:16 pm 

Why did the penguin back out of the wedding?

He got cold feet.
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Re: A seemingly intractable problem

Postby Braininvat on December 17th, 2016, 10:16 pm 

Close enough. A former 3rd grader of mine gave the answer as "because 7 8 9."
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 10:18 pm 

That's the spirit. Questions that are less intractable. Chickens crossing roads and such.
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Re: A seemingly intractable problem

Postby Dave_Oblad on December 18th, 2016, 5:59 am 

Hi folks,

Back again.. company has left. Looks like no spoilers yet.

What is Q16? Don't tell me if it will spoil the problem.

So.. unto the breach I go.. wish me luck.

Regards,
Dave :^)
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Re: A seemingly intractable problem

Postby NoShips on December 18th, 2016, 6:02 am 

Scruffy posted a link to the test on the previous page, Dave. Post #9
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Re: A seemingly intractable problem

Postby Braininvat on December 18th, 2016, 1:37 pm 

Had a solution, but it fell apart in the next-to-last equation. I may have the big circle wrong.
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Re: A seemingly intractable problem

Postby Scott Mayers on December 18th, 2016, 2:30 pm 

A friend of mine got into Mensa but then realized it was overrated. Puzzles can help one solve problems but they don't always serve anything more intellectual than to map the KIND of thinker to a 'culture'. So IQ tests are more often misleading.

I tried the OP puzzle beginning with assuming the second figure as a key. It leads to six general possible 'number' identities of zero or one. The logical relations (or 'functions') increases the complexity though. Side-by-side as one 'dimension' and the coinciding ones as some 'complementary' relationship. I tried assuming a few but gave up after a few tries over a couple hours. I assumed for numbers of the diamonds as (0 or 1) and the relationship function as addition/multiplication, then multiplication/addition, then subtraction/addition, few others. But unless I spend more time to exhaust all possibilities to 'test', the puzzle may be just misleading of any solution without knowing the context of the creators background.

I might try again later.

Possible Identities (not necessarily exhausted) for the key:

0 + 0 = 0
0 x 0 = 0
0 - 0 = 0
1 x 1 = 1
1 / 1 = 1
1 ^ 1 = 1

Complements could be:
addition/subtraction
addition/multiplication
multiplication/division
powers/logarithms

or even strictly logical ones:
and/or
coincidence/XOR
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Re: A seemingly intractable problem

Postby Lomax on December 18th, 2016, 2:38 pm 

Braininvat » December 18th, 2016, 6:37 pm wrote:Possible spoiler, but this may be only 1 of multiple solutions, and this doesn't reveal how it's obtained...

.
.
.
.
.
.
.
anyone get 3?

I got a much larger number. I'm curious how you got there - would you mind PMing me?
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Re: A seemingly intractable problem

Postby Natural ChemE on December 18th, 2016, 2:48 pm 

Lomax » December 17th, 2016, 7:30 pm wrote:
Natural ChemE » December 18th, 2016, 12:59 am wrote:That alleged IQ quiz is nothing of the sort, and the intro section of that webpage is fairly toxic. People who embrace that world view are likely to suffer as its author had.

What world view?

A lot of human knowledge seems to be communicated by inference. Like, while I've learned a great deal from literally interpreting statements from family, friends, teachers, books, the internet, etc., I suspect that I got far more from inferring models from those same sources and putting it all together.

The world view inferred from this quiz has a lot of falsehoods about what intelligence is, who's smart, what it means to be intelligent, how to socialize, etc.. They heavily imply lots of falsehoods throughout the intro, the questions, and even in the alleged IQ test's existence. It's this inferred communication of falsehoods that I find so toxic.

If I had to pick a single criticism, I guess it'd be that this "IQ test" doesn't really test reasoning skills; it's mostly just tedious pattern-matching. For example, the question in the OP of this thread isn't conceptually difficult it's essentially a big guessing game. If I wanted to solve it, I'd just write a computer program:
  1. Have guesses for all the different sorts of meanings each shape/relationship could have.
  2. Iteratively guess all possible combinations of those meanings.
  3. On each guess, evaluate all of the equations. If all of the equations happen to be true, then record that interpretation.
  4. After completing, the program would have a set of viable interpretations. Compute the final expression using each of these to find the set of answers.
Which is exactly what everyone is doing. It's just stupid and tedious, so may as well have the computer do it.

But, referring back to the conceptual problem with this alleged IQ test's very existence, the fact that this IQ test doesn't test intelligence wasn't even a problem for the High IQ Society in the first place. Those guys never needed actual intelligence as they weren't out to do anything that required it, e.g. cure cancer. They just wanted a social club that stroked their egos, and this alleged IQ test served that purpose.

PS - Just to note it, you're right that many of these questions are under-determined. In general, any open-ended pattern-matching question will have an infinite number of correct solutions.
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Re: A seemingly intractable problem

Postby Dave_Oblad on December 18th, 2016, 2:58 pm 

Hi All,

I got through all of it (in 45 minutes) except the Function of the Large Diamond.

I spent the remaining time (like about 8 hours) trying to resolve that last part.. it seems like a cheat unless I'm wrong. I sent my answer to Lomax via PM, to see if he agrees with my answer.

Lomax: Feel free to post here if I'm Right or Wrong (without giving anything away).

Problem: (ignore colors)
VALUES:SMALL,SHAPE
SS=Small Square
SC=Small Circle
SD=Small Diamond
ST=Small Triangle
FUNCTIONS:LARGE,SHAPE
(LT) = large Triangle
[LD] = Large Diamond
<LC> = Large Circle
Formulas in order as per OP:
(SS) + (ST) + SC + SC = 29
[SD]=SD
SS + (SC) + (ST) = 23
[ST,ST] = (ST) + <ST> + SS
SC + SS + SS + SS + SS + ST = 18
(SD) + (SD+SS) +SS = (SD+ST) + (SS) + SC
(SD) + (SD+SS) + SS = (SD+ST) + (SS) + SC
<SS+SS+SS> + ((SC)) = (SS) + ST + ST +SC
[SD,SC]=?

Going to bed now.. can't think any longer..lol.

Regards,
Dave :^)
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Re: A seemingly intractable problem

Postby Lomax on December 18th, 2016, 3:06 pm 

Natural ChemE » December 18th, 2016, 7:48 pm wrote:But, referring back to the conceptual problem with this alleged IQ test's very existence, the fact that this IQ test doesn't test intelligence wasn't even a problem for the High IQ Society in the first place. Those guys never needed actual intelligence as they weren't out to do anything that required it, e.g. cure cancer. They just wanted a social club that stroked their egos, and this alleged IQ test served that purpose.

Ha, well I have the same feeling about this kind of thing. I've answered four questions for myself, and now that my ego's adequately stroked I've gone back to getting on with my life. It does seem to me (and I can't tell whether you acknowledge it or not) that a lot of your criticisms can be applied to IQ tests in general. For instance a common type of question is "solve the following anagram: NDEGALN". For the most part that's a brute-force question, isn't it?

Natural ChemE » December 18th, 2016, 7:48 pm wrote:PS - Just to note it, you're right that many of these questions are under-determined. In general, any open-ended pattern-matching question will have an infinite number of correct solutions.

It's worse than that; some of the questions are completely arbitrary. Take Q6 - "calculate the value of Feynman". The only Y in the whole thing is in his name, so it can't be gotten from the other names provided. And it can't be gotten from elimination (assuming all the letters to have different values from 1-26) because there's no J, no Q, no X. So one could spend a month finding the 22 given values only to discover they've got to make up the answer for themselves, after all.
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Re: A seemingly intractable problem

Postby Lomax on December 18th, 2016, 3:14 pm 

Dave, I tried it your way originally, and wasted hours. As I say, I don't think it can be gotten by simplifying the equations and solving them against each other. Mathematically the intuitive thing to do would be to rearrange them so they all equal zero ("SC + 4SS + ST - 18 = 0", etc) and then made equivalent to each other ("SC + 4SS + ST - 18 = LT(SS) + LT(ST) + 2SC - 29", etc). I tried this and with all the help of the multi-variable calculus I learned at college (I took an advanced course, equivalent to the first half of a degree) I got almost nowhere.

It's much more fruitful to take a stab in the dark at what the values mean in equation 5 ("SC + 4SS + ST = 18") and see if your guesses yield consistent results for all the other equations. This won't guarantee you a uniquely right answer, but if it doesn't, that's only because there isn't one. The answer I got was quite aesthetically pleasing (you'll see what I mean if and when you get it) so I was happy with it.
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Re: A seemingly intractable problem

Postby Lomax on December 18th, 2016, 3:18 pm 

Incidentally, I like question 24 much more. It's straightforward, has one true answer, and (from what I've seen on the internet) is simply impossible for a large number of people to grasp, even after having the answer explained to them. I don't think it has the problems Natural ChemE identifies.

Haselbauer-Dickheiser Test wrote: A box contains two coins. One coin is heads on both sides and the other coin is heads on one side and tails on the other. One coin is selected from the box at random and the face of one is observed. If the face is heads what is the probability that the other side is heads?
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Re: A seemingly intractable problem

Postby Dave_Oblad on December 18th, 2016, 3:24 pm 

Hi Lomax,

I cheated (sort of).
I wrote a program to try all (4) value variables between -100 to +100
against
6 reasonable functions.
(The algorithm tries every combination of everything)

Everything worked perfectly but the Function for the Large Diamond.
I finally forced it but that didn't feel right.

Maybe there is a simple function for Large Diamond I didn't think of?

Wrote you a PM.. send one back when you got a moment.

Best wishes,
Dave :^)
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Re: A seemingly intractable problem

Postby Dave_Oblad on December 18th, 2016, 4:44 pm 

Well folks,

Thought I had it.. but a stupid Typo in my program resolved it wrong.
Corrected the Typo and now it won't resolve at all.. I'm missing something.
(probably a wrong/missing function)

Lomax found my Typo.. Thanks Lomax.

I had:
LT(SS) + LT(SC) + SC + SC = 29 Then Status(1) = True

It should have been:
LT(SS) + LT(ST) + SC + SC = 29 Then Status(1) = True

When all 7 Equations(OP) = True.. then solution is found (I wish..lol).

I'm going to bed. Will try again later.

Best wishes all,
Dave :^)
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Re: A seemingly intractable problem

Postby Dave_Oblad on December 19th, 2016, 9:27 am 

Hi Everyone,

Ok.. spent another 3 hours on the problem and solved it. Or at least I found a solution that works. There may be multiple solutions. I sent my solution to Lomax to verify and find out if it matched his.

Note: Hints below are applicable to my solution.. keep that in mind.

Hint: The Functions are not atypical of what I would call Functions. I also found two different Variable Symbols that had the same value.. that doesn't seem fair.. but see no rules against it. Couldn't resolve 29,23,18 otherwise.

Hint: I ended up with 4 Variables and 6 Functions.
(yep 6.. size does seem to matter)
(Ok, technically only 4 functions because 2 are neutral)

Good luck to anyone still trying.

Note: Required much more successive approximation hand tweaking than Brute Force computer searching all possibilities. I may still try that approach to search for alternate solutions.. but the program could take many hours to run (like 10 hours or more depending on arbitrary restraints).

Hope Lomax will confirm my solution.. even if it doesn't match his.

Best wishes,
Dave :^)
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