Radiometric dating simplified
All that was just to say: be excited, the way you tie your shoes is only possible in universes similar to (with the same number of dimensions as) our own.
You can’t tie a knot in a string in two dimensions and a knotted string in four (or more) isn’t really knotted at all.
Each step has its own individual half - life but the first decay to Th 234 is about 20,000 times slower than the other decay steps.
Those of you who are familiar with chemical kinetics will know that it is the slowest step in a mechanism which determines the overall rate of reaction, the so - called "rate determining step".
The image here is only a cross-section of such a knot.
It turns out that if you have an ordinary knot, you can use it to create a higher dimensional knot. There’s “suspension“, which usually doesn’t work (the created knot is often not a “manifold“, which is kinda cheating), and there’s also “spinning” which always works.
In part because once you’ve connected the ends of your string the knot you’ve got is the knot you’ve got, and that invariance is very attractive to math folk.
Left: In two dimensions, no matter how complicated and convoluted your string is it can never be tied in a knot.
Sometimes that math is fairly easy and even intuitive.
Sometimes a group of scientists will get really involved with a particular subject and kinda disappear up their collective butts for a while (especially mathematicians).
Eventually one of them will emerge like a prairie dog and bark “fellow dudes and dudesses, we should really send a message to the world so they don’t worry about us” at which point a summarizing paper such as this or this is written (about higher dimensional knots in this case), in an attempt to convey to a The tied sheets painting is by Teun Hocks and is from here. The spun knot picture was lifted remorselessly from the second paper mentioned earlier.
But if you have access to another dimension (“dimension” basically means “direction”), then you can get the dot out.
In exactly the same way, if you can “lift” part of a regular knot into a fourth dimension it’s like opening the loop and you’re free to untie your knot in the same way you’d untangle/untie anything.
1-spheres can be tied in knots in three dimensions (these are known colloquially as “knots”), which means that they can actually be created.