Hacker News Reader

Comment by js8 | Hacker News Reader

I feel like this is a trick in many wood & string puzzles.

Not quite, since most topological transformations can’t be done on actual physical objects. (I would love to see some of those wood and string puzzles try to implement some of these style of topological puzzles though, that would be awesome if it was possible.)

Most of the wood and string puzzles fall under knot theory specifically, rather than topology. The main trick I’ve seen used in those puzzles is they have knots with an even number of crossings and therefore they can be separated (I believe the formal term might be “they have ambient isotopy to unlinked unknots”, but there’s a lot of subtlety I don’t get, so that’s probably wrong) but the knots are deformed to look like two distinct knots, each with an odd number of crossings (a knot with an odd number of crossings cannot be separated). Our intuition tells us “one inseparable knot plus another inseparable knot equals a single, bigger, still inseparable knot”, but that’s knot the case.

I'm not sure exactly what you're trying to say (I'm not sure what you mean by "separate" here), but your assertions seem incorrect. Knots can have even or odd crossing numbers, that alone will not tell anything about whether it is an "unknot" or not. Also, if you have two non-trivial knots and "join" them (ie each a knot in a circle, cut each circle in one spot and join the circles at the cuts) you will _never_ get an unknot.

Yeah, as I thought, I don’t know knot theory nearly well enough to use their terms properly.

I had the same initial impulse, but I think the transformation 1 -> 2 can't work irl. especially if those are compact solids.

Edit:

2->3 also seems impossible. you basically move the hole around.

You can do it IRL with something like plasticine.

No, you can't do this trick with wood and string. Try tracking what would happen to the "string" joining the two loops.

Reply on news.ycombinator.com