The subfield of “knot theory” in math as a kind of geometry of “twistiness” gives us a deep “meta-intelligent” signal or lesson.
Meta-intelligent means “perspective-challenging” with or without full details of any subfield itself.
Consider this overview or comment on “knot theory” now:
“In mathematical knot theory, you throw everything out that’s related to mechanics,” Dunkel (MIT math professor) says. “You don’t care about whether you have a stiff versus soft fiber—it’s the same knot from a mathematician’s point of view. But we wanted to see if we could add something to the mathematical modeling of knots that accounts for their mechanical properties, to be able to say why one knot is stronger than another.”
But you immediately think: in the real world knots are not only twisted up in mathematically definable ways but are in fact actual shoelaces, neckties, ropes, etc, that have chemical and molecular properties before you describe their twist-and-tighten or slide-and-grip “shapes.”
Which is the real: the math or the “ropiness” of the ropes or the “laciness” of the laces?
The relationship between things and numbers is elusive.
Mathematicians have long been intrigued by knots, so much so that physical knots have inspired an entire subfield of topology known as knot theory—the study of theoretical knots whose ends, unlike actual knots, are joined to form a continuous pattern.
In knot theory, mathematicians seek to describe a knot in mathematical terms, along with all the ways that it can be twisted or deformed while still retaining its topology, or general geometry.
MIT mathematicians and engineers have developed a mathematical model that predicts how stable a knot is, based on several key properties, including the number of crossings involved and the direction in which the rope segments twist as the knot is pulled tight.
“These subtle differences between knots critically determine whether a knot is strong or not,” says Jörn Dunkel, associate professor of mathematics at MIT. “With this model, you should be able to look at two knots that are almost identical, and be able to say which is the better one.”
“Empirical knowledge refined over centuries has crystallized out what the best knots are,” adds Mathias Kolle, the Rockwell International Career Development Associate Professor at MIT. “And now the model shows why.”
As per usual in science, one is dazzled by the ingenuity of the quest and the formulations but puzzled by the larger implications since we can never decide whether math “made” us or we “made” (i.e., invented) math.