How Far Can We Change Our Starting Assumptions?

There's a periodic table of knots, yes. And the way that they decided to classify them was, if you've got a knot, you try and put it down with the fewest points where it crosses itself. So there's only one knot that has a minimum crossing number of three. There's only one at four, two at five, three at six, and then you get more and more very, very quickly. By the time you get up to aminimum crossing number of nine crossings, there are forty nine distinct knots. If you were to list out all of them, up to 16 crossings or fewer, there are over one point seven million possible knots. They missed loads.