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MU puzzle

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Re: MU puzzle

#11

Post by hermitdev »

Torkel wrote: post #6
lixtra wrote: post #4

When I read about it in Gödel Escher Bach I wasn’t aware yet that unsolvable is a valid answer to a problem. I felt cheated(1) and the whole book lost a lot of its appeal. In retrospect it may have actually undone some damage done by the school system where the solution space is usually very restricted. Edit: (1) From what I remember it’s stated as find the sequence and not does such a sequence exist.

I have a similar memory! I read about the problem in the book and worked on it for days, trying to solve it. I was in junior high at the time, and my math teacher spotted what I was doing. The teacher figured out quite quickly that it was impossible to solve. And I felt sort of dumb for not figuring out it was impossible and having a teacher prooving it :)

I wouldn't feel dumb about it. People often look at very difficult problems for a very long time before they conclude a solution is impossible and later to be disproven. I would expect this one to be any different. Yes, there are currently no known solutions, but that doesn't preclude a brilliant mind coming in down the road with a solution.

Re: MU puzzle

#12

Post by hermitdev »

jamescostian wrote: post #9
Intermernet wrote: post #7

Earlier quoted context omitted.

On a slight tangent, I recently read a paper on an interesting relationship between Collatz path length and Mersenne primes. "Our main finding to report is the fact that a path length of a Mersenne prime is approximately proportional to its index for large n, namely, D(Mn) ≈ 13.45n." Paper is at https://arxiv.org/pdf/1104.2804.pdf . WARNING: PDF.

I'm curious, why do people on HN warn about PDFs? The worst things I can imagine happening with PDFs are (1) you don't have any software that can read it (probably like .2% of HNers?) and (2) it could potentially have some malware (but the same could be said of a website)

Adobe is not known for their security. PDF is also known to allow remote execution via PDF. Default reader on most systems being Adobe's reader, yeah, I'd avoid it. I know this is shifting as browsers incorporate readers, but the format is tarnished.

Re: MU puzzle

#13

Post by geofft »

jamescostian wrote: post #9
Intermernet wrote: post #7

Earlier quoted context omitted.

On a slight tangent, I recently read a paper on an interesting relationship between Collatz path length and Mersenne primes. "Our main finding to report is the fact that a path length of a Mersenne prime is approximately proportional to its index for large n, namely, D(Mn) ≈ 13.45n." Paper is at https://arxiv.org/pdf/1104.2804.pdf . WARNING: PDF.

I'm curious, why do people on HN warn about PDFs? The worst things I can imagine happening with PDFs are (1) you don't have any software that can read it (probably like .2% of HNers?) and (2) it could potentially have some malware (but the same could be said of a website)

Before the advent of built-in PDF readers in browsers, it would often either trigger a download or launch an external program, which are kind of rude behaviors to spring on someone without notice. I still have this habit (though I'll just mention "(PDF)" in a parenthetical), and I'll certainly warn about autoplaying audio or an excessive amount of ads even if I expect a good fraction of readers to have browser configs/extensions to deal with those.

Re: MU puzzle

#14

Post by amatic »

Is the Gödel Escher Bach worth the reading? I started, but I feel it's fluff. People say he is good, though. Are there some practical insights?

Re: MU puzzle

#15

Post by afthonos »

hermitdev wrote: post #11
Torkel wrote: post #6

Earlier quoted context omitted.

I have a similar memory! I read about the problem in the book and worked on it for days, trying to solve it. I was in junior high at the time, and my math teacher spotted what I was doing. The teacher figured out quite quickly that it was impossible to solve. And I felt sort of dumb for not figuring out it was impossible and having a teacher prooving it :)

I wouldn't feel dumb about it. People often look at very difficult problems for a very long time before they conclude a solution is impossible and later to be disproven. I would expect this one to be any different. Yes, there are currently no known solutions, but that doesn't preclude a brilliant mind coming in down the road with a solution.

In this case, there is provably no solution. A brilliant mind can’t fight that, any more than it can prove that 2+2=5. :-)

(Yes, using the traditional definitions of all those symbols.)

Re: MU puzzle

#16

Post by ineedasername »

toastking wrote: post #8
lixtra wrote: post #4

When I read about it in Gödel Escher Bach I wasn’t aware yet that unsolvable is a valid answer to a problem. I felt cheated(1) and the whole book lost a lot of its appeal. In retrospect it may have actually undone some damage done by the school system where the solution space is usually very restricted. Edit: (1) From what I remember it’s stated as find the sequence and not does such a sequence exist.

I always saw it as his way of teaching of grammars. But I think it is kind of bad that the grammar isn't actually creating a solvable system.

it is kind of bad that the grammar isn't actually creating a solvable system

But that was precisely the point. That given a system with a set of rules, the space of all possible problems may be larger than the space of all solutions, i.e., not all problems have a solution.

To say it's useful to be able to determine if a problem is solvable is a vast understatement.

Re: MU puzzle

#17

Post by ineedasername »

chongli wrote: post #5
lixtra wrote: post #4

When I read about it in Gödel Escher Bach I wasn’t aware yet that unsolvable is a valid answer to a problem. I felt cheated(1) and the whole book lost a lot of its appeal. In retrospect it may have actually undone some damage done by the school system where the solution space is usually very restricted. Edit: (1) From what I remember it’s stated as find the sequence and not does such a sequence exist.

I would continue arguing that "unsolvable" is not a valid solution to this puzzle . If the description asks you to "find the solution" and the solution does not exist, then it is a riddle, not a puzzle.

You're simply playing semantics and defining "puzzle" as "something that has a solution".

But if you're at work and your boss says "I have a puzzle I need you to solve: Given these constraints, find an answer" You need to be able to say "Here is my solution" or "No solution is possible, and here is why."

Or take something simpler: a 500 piece "Puzzle" only there's a manufacturing defect in all copies: one piece is miss shaped. The puzzle can't be completed; there is no "solution". It's still a puzzle.

So no, you don't get to "unfair!" your way out of the MU Puzzle through narrow semantic definitions, especially given the, well, grammatical nature of language, because then you have gone and missed the entire point.

Re: MU puzzle

#19

Post by reificator »

lixtra wrote: post #4

When I read about it in Gödel Escher Bach I wasn’t aware yet that unsolvable is a valid answer to a problem. I felt cheated(1) and the whole book lost a lot of its appeal. In retrospect it may have actually undone some damage done by the school system where the solution space is usually very restricted. Edit: (1) From what I remember it’s stated as find the sequence and not does such a sequence exist.

See, that's on my reading list. (3rd or 4th I think, so coming up soon)

Now I've had some of the surprise ruined just by reading a HN thread that didn't even appear to be related to the book in the first place. If I had just clicked the Wikipedia link and read the first puzzle, I'd have clipped it to my notes and marked it as something to read afterward. But because this was pushed up to top comment, it caught my eye first.

Re: MU puzzle

#20

Post by edflsafoiewq »

amatic wrote: post #14

Is the Gödel Escher Bach worth the reading? I started, but I feel it's fluff. People say he is good, though. Are there some practical insights?

I think most of us who really like it read it as kids which colors it too much. I distinctly remember this proof that you can't solve the MU-puzzle as the first piece of mathematics I ever saw. In one swoop I discovered impossibility proofs, invariants, and the use of divisibility which suffused the whole book with an aura of initiation into great mysteries that it will never attain for the already-initiated.
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