[lixtra]

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.

[chongli]

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.

[starbeast]

The puzzle is called MU for a reason. 'Mu' is the valid solution. https://en.wikipedia.org/wiki/Mu_(negative)#The_Mu-koan

[ineedasername]

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.

[paradoxparalax]

I think his point: "If it asks you for a solution that doesn't exist, It's a Riddle" is a perfectly valid point and your comment was a bit "overreactive", in my opinion.

[ineedasername]

What makes it a valid point? I see nothing in the definition of either word that would definitively preclude "puzzle" as an appropriate label. Riddle is fine too, but no mutually exclusive.

You and the parent comment claim it's not a puzzle, it's a riddle, with the implication that's somehow unfair or deceptive in how the problem was framed.

That is a semantic hair splitting that dodges the problem & its answer. In real life problems you don't get to define away responsibility for problems put in front of you. And if thoroughly stating my case is "overractive", then I'm guilty, but I find it's generally better to over-support my argument than state claims without justification.

[Svettie]

Different contexts. In the real world it's understood that anything is possible (you can also clarify if unclear). But in a book like this, you put trust in the author to use precise language, and especially given the nature of this particular book. Maybe it was done purposefully for effect, but that's still jarring.

[ineedasername]

No. In the real would "anything" is not possible, and that it is an odd statement to make. It's not at all uncommon for me to see or be a part of a problem solving process that at some point includes a statement like "given the constraints we're under, there is no current solution." Now the next stage might be something like "We can eliminate one constraint by doing X, which will cost Y dollars" etc. So in the MU problem one might say "Given the string transformation rules, MI cannot become MU. However, if we added rule X, then such a transformation would become possible."

All of which is besides the point: "Puzzle" and "Riddle" are pretty much interchangeable. They appear as synonyms for each other in thesauri; "riddle" is given as one of multiple definitions for "puzzle" in wiktionary. Many sources treat "riddle" as a kind of "puzzle". The degree to which riddle might be more appropriate in a given context relies on a few factors, for example riddles often tend towards more verbal basis, spoken or written. A puzzle is the broader category and can include things like physical object such as a 500-piece jigsaw puzzle. But any difference is still only that of broader category and specific type. Either term is valid here.

So stating "It's not a puzzle, it's a riddle" is indeed splitting hairs, or simply not knowing the nuances of the actual definitions of those words. The OP of that comment appeared to be doing so with the implication that the whole problem was somehow unfair as a result. I cry foul on that assertion for the reasons stated.

[gus_massa]

It's a book about incompleteness, undecidability and other nasty surprises in math. Nobody expected them. So an unexpected nasty surprise of an unsolvable problem is somehow relevant to the book.

[kassouni]

I think this points to the central idea Hofstadter was trying to communicate. In order to "solve" the puzzle, you have to exit what he calls the "mechanical (m) mode" and think about the puzzle on a different level, the "intelligent (i) mode." The goal was for the reader to try and solve it by realizing blindly applying axioms of the system got nowhere. Proving the puzzle is impossible requires a mode of thinking analogous to Gödel's incompleteness theorem.

[Torkel]

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 :)

[Normal_gaussian]

There are a whole class of problems that revolve around the incompatibility of operations based on the primes (in this case 2 and 3). When you attempt to solve, and fail to solve, any of them you are likely to gain an instinctive appreciation for all of them - the kind of appreciation that would lead a maths teacher to a proof to the contrary very fast.

It should be noted that if the teacher had had the foresight (often a big ask) to simply tell you they suspected there was no solution, which is often the case with such problems presented as they are, and that you should attempt a proof alone, you would likely not feel so bad about not spotting it immediately.

[hermitdev]

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.

[afthonos]

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.)

[toastking]

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.

[ineedasername]

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.

[reificator]

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.