Exploring the Math of Dimensional Knots

[dsrw]

Hey all, i don't know if this is the right forum for this but i think there is a branch of math that studies knot and i just have few questions.
Today i was untying a knot and then i though, maybe it would be easier to untie a 3D knot in a 4D world (not time). Am i right? Since nobody can visualize a 4D dimention, so i simplified to 2D knot in 3D, then i realize you cannot have a knot in 2D, the string has to cross itself(entering 3D) at least once to become a knot.
Then further, how much a higher dimention knot look or act like in a lower dimention, or does that not even apply? Anyway just few questions that bugged me the whole day, thanks for reading!

 

[Antiproton]

The branch of mathematics you're thinking of is Topology, or, more specifically a subfield of Topology called Knot Theory. And, I think, the dimensonality your thinking of isn't what the mathematicians are thinking of. I won't say any more, as I earned a C+ in topology. I'll leave it to my colleagues.

 

[tacman]

Hi there,

You are absolutely correct that there is a branch of math that studies knots, called knot theory. It is a fascinating and complex field that has applications in various areas such as physics, biology, and computer science.

Your question about whether it would be easier to untie a 3D knot in a 4D world is an interesting one. In some cases, it may be easier to untie a knot in a higher dimension, but it also depends on the specific properties of the knot itself. In fact, there are some knots that can only be untied in higher dimensions.

As you mentioned, it is difficult for us to visualize higher dimensions, so mathematicians often use analogies and projections to study them. For example, as you pointed out, a 2D knot in 3D cannot exist without crossing itself, so it is not a true knot. Similarly, a 3D knot in 4D may have properties that cannot be fully understood in 3D.

In terms of how higher dimensional knots may look or behave in lower dimensions, there are some interesting connections and relationships, but it is a complex and ongoing area of research.

I hope this helps answer some of your questions and I encourage you to continue exploring the fascinating world of dimensional knots. Happy knotting!