That's how I like to explain it to people, though there's a small caveat that doesn't really affect the argument, but it's worth considering. The only times a

That's how I like to explain it to people, though there's a small caveat that doesn't really affect the argument, but it's worth considering. The only times a knot-with-hues actually corresponds to a knot in Euclidean 4-dimensional space are when you can smoothly modify just the colors to make the knot be monochromatic. For example, if the knot goes through the whole color wheel of hues, 0 to 360 degrees, then that corresponds to a knot in a different space (R^3 x S^1). (A way to avoid this problem is to not use the color wheel, but instead use, say, wavelength of a spectral color.) Although there are no nontrivial circle knots (S^1 knots) in R^4, there are nontrivial sphere knots (S^2 knots). That well-advertised Quanta article about Lisa Piccirillo's work is about this sort of thing.