So, you are about to write the sequence of Leibniz s "Monadology", and invent a

*universal knotting machine* able to compute, and, why knot, to

*think*, and to

*replicate itself*, using, as elements, the elementary knot transformations that leave the knot topologically invariant ( the Reidemeister moves )( or retain any other invariant property of the knot ). ! ! ! Oh, my knotGod ! This IS an abstract idea, indeed ! Von Neumann would be proud of it !...

William Thomson ( Lord Kelvin) tried to explain the atoms by knots, but it turned out that God had not utilized his idea. We can imagine intelligent beings at another Galaxy, that think using knot-brains made by tangles of one-atom-thin chains, transforming into zillions of curvilinear shapes, that is, thoughts... Even beyond this, may be their knot-brains will be made by quantum particles, able to perform quantum computations. (1) If a classic brain, made by classic objects, can be so irrational and stupid as the brain of humans, we can imagine how irrational and stupid will be a quantum brain !

In this Forum I believe we are still a little more modest. We would be happy if somebody would help us enumerate all the bends made by two interlocked overhand knots, for example... We are not experts on mathematical Knots or on Artificial intelligence. and I doubt if we are experts even on practical knots ( we still do not know which Sheet bend is stronger ! ), or on plain intelligence ( we can not agree on anything ! ).

1. Computing with quantum knots. by G.P.Collins

marcuslab.harvard.edu/otherpapers/SciamTQC.pdf