What is Topology, and what's the big deal?

Here is a link to a google books copy of some of Kauffman's book: http://books.google.co.nz/books?id=av05vRwIKIwC&pg=PA85&source=gbs_toc_r&cad=3#v=onepage&q&f=false

It skips the first 30-odd pages, which is a bit of a shame because that's where the bracket state formalism is explained; there, Kauffman writes out the states for the trefoil knot, the Hopf link, and then uses the results to write more complex knot states.

Another document: http://homepages.math.uic.edu/~kauffman/RTang.pdf is a bit easier to get into, it has a section on bracket polynomials which is much the same as the missing introductory chapters in the online book.

What is knot theory? That's a bit difficult to answer given Kauffman's book as a reference because it seems to cover a lot of different ideas. But that's half the fun, trying to find out what the big deal is, eh?

 

Log in or Sign up to hide all adverts.

The problem with mathematics is that it is abstract.

Take a look at sets for example. Sets are obviously abstract as are the mathematical symbols that are used in physics. Also take a look at points, dimensions and coordinate systems.

Points, coordinate systems and dimensions are also abstract things devoid of any physical existence. Are you saying that there is such a thing as a point in nature? What about numbers? Do you think that sets and numbers are physical entities? What about coordinate systems? Do you really think that coordinate systems are physical entities that have a real physical existence?

Mathematics is not a good tool to describe nature because mathematics is abstract and nature is physical and deals with physical entities, not abstract ones.

 

Log in or Sign up to hide all adverts.

I, and everyone whose opinion I value on this matter, disagree with you.
https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

http://schneider.ncifcrf.gov/Hamming.unreasonable.html

But this seems off-topic to me.

 

Log in or Sign up to hide all adverts.