The puzzle involves getting a ring on one side of a roped trestle to the other.The 10-minute vid is cute as an amateur, physicist, and one other savant take whacks at it until it is solved by a member (chief?) of the Japanese Ring Puzzle Association, which is nice to know is a thing.
It seems to me that some mathematicians (knot-specialists are subsumed under the topology profession, right?) cut their teeth on this stuff, and I’d like to know if any of the knowledge involved can be simplified here to get a feel for what’s involved. (FWIW, when I learned how to tie a half-Windsor knot I was on an intellectual high for a week, let alone a sartorial one.)
A topologist would be eminently qualified to tell you that a solution exists. But topological techniques would be of no use in finding it, unless all of the parts of the puzzle are made of rubber.
I remember that puzzle. Some games dealer at some show I was at (a D&D show or something) had one on a table, and had a prize if you could solve it. I was 14 or 15 and solved it in about 5 minutes. I am not good at advanced math, but I am good at those kind of puzzles.
I can also put that star back together, and I refuse to believe that anyone really thinks that’s hard.
As an intellectual exercise, could he look at that thing and formalize it on paper 1-2-3?
Surely the real world break points (constraints) at allowable/feasible transformations tactics, which when added together map out the solution, is part of the territory?
If not topologists, for whom? Don’t physicists also think about things like that?
Well, some physicists are certainly good at these puzzles, insofar as I’m a physicist, and I’m good at them. But I don’t think that the skill set involved in doing them particularly relates to physics at all.
If there’s any professional domain that does particularly relate to these puzzles, I’d guess that it’d be some form of engineering.
If you needed an automatic solution, you could— probably— write a computer program to solve the puzzle along the lines of computer programs that calculate how to navigate a sofa through a narrow hallway, or the ones that untangle complicated knots.
I could be wrong about that, but if not then there would be applied mathematics and numerical modeling involved.
I mean, the same topological proof that tells you a solution exists also tells you what it is… And then you go try it and it works.
Sure, in topology you consider allowing arbitrary stretching and whatnot, and with the physical puzzle here, you can’t do arbitrary stretching and whatnot, but if you’re willing to allow the topologist to be considered as proving the existence of the solution, why not also allow them to be considered as demonstrating what it is?
In practice, give this puzzle to the right kind of topologist and they’ll solve it, no problem.
I didn’t look at it (wasn’t interested in spending 10 minutes on it), but there is a knot invariant, called the knot polynomial, that would tell you if it can be done without telling you how to do it. But it is not a topological question since to a topologist, all knots can be unknotted. The reason is that a topologist can cut and paste, provided only that things that started out together ended up together and vice versa. Never mind what happens in between. What you need to unknot is to continuously deform it into a circle.
Perhaps I was speaking a little too strongly when I said that a topologist could say that a solution exists. By that, I simply meant showing that the solved state has the same connectedness as the initial state. But showing that does not necessarily imply that there’s any physical way to get from one to the other, and in fact it’s very easy to make a “puzzle” where the connectedness is the same but there is no physical solution (for instance, one piece being a barbell and the other being a ring around the central bar, with the object of removing the ring).
Sure, but topologists consider questions of not just “Are these topological spaces homeomorphic?” but also “Is there a homotopy from this to that?” too.
This response similarly confuses me, in that I consider knot theory to be a part of “topology” and knot theorists to be “topologists” too.
As an empirical matter, there are mathematicians who would consider themselves “topologists” to whom you could show this problem and have it be simple work for them because of the very studies they engaged in which led them to consider themselves “topologists”.
But nevermind the name of the field. The OP’s question is as to whether there are mathematicians who study the appropriate sort of thing for which this puzzle would be straightforward. And the answer to that is, yes.
The only caution I’d give about what the math specialists are called who work on the math of this, is that in the real world, there are lots of puzzles and problems which are, like this one entirely inconsequential in terms of getting through life, but which are specific challenges for theoretical people to find a way to deal with using their particular skills, in order to apply the “solutioneering” so to speak, elsewhere.
It’s a bit like when some athlete decides to see if it’s possible to climb Everest in a tutu or some such.
Like the other fellow above, I solved this puzzle myself long ago, though not as fast. I have absolutely no education or expertise in using math or other modeling approaches to deal with such, but like the other fellow (I suspect), I knew the SOCIOLOGY behind the creation of such puzzles. They aren’t so much DIFFICULT, in the sense that no special tools or education is needed, you just have to think of how to solve it from a different point of view. In the case of this puzzle, as I recall, you stop trying to move the ring from place to place, and instead find a way to move the ROPE from place to place.
The headline on the video is nonsense, or at least misleading. No one had to work for ten years to solve the puzzle. Maybe it took ten years to figure out how to program a computer to do it.
These techniques are part of the field of computational topology (PDF), which would be the branch of math/engineering/CS that you’d need to analyze this problem. For example, one of the classic problems of computational topology is to figure out whether a robotic with a certain number of joints and a certain number of constraints can move an object from point A to point B. Topologically, this is asking the question of whether the initial and final configurations of the robot & object are in the same “connected component” of the configuration space. One could presumably apply the same sort of algorithms to a rigid puzzle.
I’m on the “no” side in a way. Some Topologists could solve. Many won’t.
The mentality required to solve these involves more than just Topology. The ropes, etc. are not arbitrarily stretchable. Particular sequences of moves are required to solve it.
Take my favorite “simple” 2 piece puzzle. Topologically it’s a no-brainer at all. If the metal was flexible it’s a completely trivial task. But it takes a surprising number of moves to solve.
Some topological thinking really helps the rope-style puzzles. Once you figure out what can’t be done, what remains must be the solution. It’s just a question of getting things moved around to allow that to happen.
I’m generally pretty good at these types of puzzles. Any time someone brings something like this into work and plops it on my desk, I’m pretty much done with work until I solve it. Fortunately for my employers, that’s usually only maybe ten minutes or so worst case, at least so far. I haven’t seen this particular puzzle before, but I have quite a few similar types of puzzles at home.
I don’t approach them from a topology point of view. When I first look at the puzzle, I want to know what can move where and what influences what else. One big hint is that these types of puzzles only include as much rope as is necessary to solve the puzzle. If there’s that much slack in the rope, you’ll use all of it up at some point. So you need to start figuring out where you can move the rope (putting it through the hoop and such) and what its limits are.
There is a bit of topology involved, because at some point you need to visualize what is happening between the ring and the rope, and you need to be able to recognize if your rope that is twisted around and through hoops and looped around etc. has actually made it to the other side of the ring, topologically speaking.
Mostly though, it’s a puzzle, and you need to figure out the trick to it. Being able to visualize the topology is important for recognizing when you’ve discovered the trick, but the main thing is figuring out what can go where within the limits of movement, not the topology.
All these non-topologists keep saying “No way”. Can we get a topologist to give their opinion? A homotopy theorist or a knot theorist or whatever? (I do give Hari Seldon’s opinion credibility, but I also find its terminological nitpick surprising…). Yes, the pieces aren’t arbitrarily deformable, but for the most part, that doesn’t matter for this puzzle; the appropriate constraints (e.g., rope can’t pass over the base) are readily formalized in the same manner as one does when considering knots in general.
I recall once going to dinner with a topologist who delighted in noting how a similar puzzle was readily solved with standard homotopy theoretical machinery, for what it’s worth.
Probably, if it’s a professionally-manufactured one. But sometimes you’ll see a homemade one where the maker just made sure that it works, without measuring precisely.
The first time my uncle ever saw the ox-yoke puzzle, the guy who gave it to him told him that the object was to get the two beads on one loop. So that’s what he did: He handed it back with both beads on one single long loop, with the rope completely untied from the middle hole.
It’s just a question of getting things moved around to allow that to happen.