from the more-than-taking-a-look dept.

[Doug Mounce]

Claim (h/t @teortaxestex) “Most blind mathematicians work in geometry and topology. It is argued that the spatial intuition of sighted people is degraded by the triviality of retinal perception.”

https://www.ams.org/notices/200210/comm-morin.pdf

[jaraymaker]

Doug,

 

I followed your link and found this reference to "knot theory":

 

"It is curious that the birth of knot theory is the result of a scientific flop: the attempt by Lord Kelvin in 1867, to model atoms by knots, which led Tait to establish the first table of alternating knots. What are the central problems in knot theory, nowadays?....."End quote

 

Googling led to e. .g

"Knot theory, in mathematics, the study of closed curves in three dimensions, and their possible deformations without one part cutting through another." End quote

 

In your estimation, is there  any (or what) relevance or application (might there be) of knot theory beyond esoteric math studies?

 

This link, https://math.mit.edu/research/highschool/primes/circle/documents/2020/Ayinon_2020.pdf speaks of the relevance of knot theory to DNA.....

 

John

[jaraymaker]

Just a bit of a follow-up to be found in the last link below; one does find this relevant, interesting "connection" between math and how DNA works in nature:

 

"Topoisomerases are a type of enzyme known for altering the supercoiling of DNA strands. They solve the problems encountered when trying to untangle a knotted strand of DNA. While in knot theory, mathematicians cannot break the knot or have the strands pass through one another, these enzymes do not have to follow these rules when untangling DNA. The topoisomerases act by quickly severing a given number of DNA strands and recombining them in a new fashion. The number of strands severed and recombined relates closely to the unknotting number of that knot. In fact, if a strand of DNA is not equivalent to the unknot, there is no possible way to make it into a simple loop without passing the strands through one another by cutting them. These enzymes can also perform operations on DNA strands, similar to the three Reidemeister moves, in order to unwind the tangle of DNA." end quote. I would say that IS relevant....   John

 

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[Doug Mounce]

John, you might add the modern concern about why my headphone wires keep getting "knotted"! haha  Topology is like geometry, but without the concept of distance and angles, so objects are like rubber and can be stretched, twisted and deformed without cutting and pasting.  It's basically set theory, and that means there are going to be lots of applications.  Image manipulation, robot motion, geographical mapping, and biology, like you mentioned.  I guess what interested me was how these different ways of "seeing" the world matter when most of us mostly think in the same way most of the time.  cheers,

~/

https://staff.washington.edu/mounce/

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