The (reasonably simple) TIB single and double loops, those we already know and those that we can/will find, are many, indeed - but not sooo many ! Dozens, but not hundreds... When one starts tying them, one by one, he will discover that he will soon learn to pass from the one to the other ( and then from every one to every other) with transformations similar to the ones we have seen in this thread, rather easily, and quickly. It might seem a huge mountain when seen from a distance, but a few steps towards it will show it is but a small hill. The interlocked overhand knot bends, for example, are many more, and their enumeration is much more difficult - and that is why it has not been achieved yet.
Of course, it needs a systematic/exhaustive way of exploring things, so one will not miss something important in his way. I believe that Luca, as well as Alan Lee, have already done fine systematic work, and they can very well finish this job they had already started !
