Imagine talking to someone from a civilization which had not developed the concept of number the way that we have. How would you begin to explain to them what numbers are, how to distinguish between them, classify them, what the relationships among them are, etc. In Knot Arithmetic , the ideas of adding and subtracting knots is discussed, but there is no mention of multiplication or division. Invent your own new operations for knots or for numbers. This is the question that pervades all inquiries in mathematics.
Mathematical truth is founded upon the ideas of logic and proof .
When students dip a wire-frame knot into a detergent solution what comes out is a Siefert Surface . If, after 50 trials, the knot produces the same Siefert Surface, student can make a good probabilistic argument that the next trial will product the same result.