4 ms·

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

by js8 4y ago

leto_ii 4y ago
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.
- chmod775 4y ago
  You can do it IRL with something like plasticine.
OscarCunningham 4y ago
No, you can't do this trick with wood and string. Try tracking what would happen to the "string" joining the two loops.
fwlr 4y ago
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.
- SetTheorist 4y ago
  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.
  - fwlr 4y ago
    Yeah, as I thought, I don’t know knot theory nearly well enough to use their terms properly.

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

by js8 4y ago

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

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.

chmod775 4y ago
You can do it IRL with something like plasticine.

OscarCunningham 4y ago

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

fwlr 4y ago

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.

SetTheorist 4y ago
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.
- fwlr 4y ago
  Yeah, as I thought, I don’t know knot theory nearly well enough to use their terms properly.